The Fall of France is one of the most ( in my opinion) interesting campaigns of World War Two, since that is when it became evident to everyone that this was not just going to be World War One V.2.0. As for why France fell so quickly? Well there are quite a few reasons why France and Britain were unable to beat back the Germans this time around.

Background:

I know most everyone and their grandmother must know about the background to the Second World War, but for those who are unaware, the British and French declared war on Nazi Germany on September 3rd, 1939, in response to the German invasion of Poland. Now France and Britain couldn't have done a whole lot to help Poland, as Germany had completely taken the country over in a month, Poland's plan to use the rough terrain in the Eastern part of its country was taken away when the Soviets invaded from the East. France did launch a small local offensive, known as the “Saar Offensive” but it essentially amounted to a small incursion into Germany, and then immediately turning around and going home (I'll cover why they didn't go further in a bit). The period in between the invasion of Poland and the Invasion of France and the Low Countries is generally called the “Phony War” although, one American journalist humorously referred to it as the “Sitzkrieg”.

The German Planning:

The first major reason for France's fall has to be Germany's plan of attack, it was a simple plan, but surprisingly effective.

The planning for the German offensive is one of the more interesting little stories of the war. Hitler ordered his men to begin planning a large scale offensive into the West a few days after Poland officially surrendered. Hitler initially wanted the offensive to start as early as November, but the German general staff managed to talk him out of it, citing the fact that the majority of the Wehrmacht was still in Poland, and that November was no time to launch such a large scale offensive. The OKH (the German general staff in charge of the ground forces) were filled with men who simply did not think a war in the west could at all be successful. The two main culprits here were the head of the OKH Walter Von Brauchitsch and his number two man Franz Halder. Neither of these men thought that France could be beaten and that any campaign in the west was going to be a repeat of 1914. So worried were they about the prospect of invading France that they contemplated launching a military coup and ousting Hitler, but eventually Hitler used power of persuasion to make Brauchitsch see things his way, and Brauchitsch began to plan for the invasion of France. Hitler sent out peace offers to both Britain and France, they were serious offers but the terms essentially amounted to: “leave me alone, and I will leave you alone”, this was unacceptable to Britain and France. Finally Hitler issued Furher Directive NO.6 on October the 3rd, 1939; it stated that the purpose of the offensive in the west was:

to defeat as much as possible of the French Army and of the forces if the allies fighting on their side, and at the same time to win as much territory as possible in Holland, Belgium, and Northern France,to serve as a base for the successful prosecution of the air and sea war against England and as wide protective area for the economically vital Rhur

So you can see that Hitler's goals at the time were “modest”, and the plans the general staff drew up reflected that. The plan was essentially a rehash of the old WW1 Schlieffen plan. Germany was to make a strong thrust into Belgium, there was a minor difference in that instead of trying to take Paris, the Germans would pause in Belgium and Northern France and wage an air and sea battle against Britain. The plan went through some minor revisions, but for all intents and purposes would remain the same. Hitler wasn't thrilled with the plan, but it was the only one he had and so he went with it. Two developments would contribute to the death of this plan.

Firstly a plane carrying details of the plan was forced to land in Northern Belgium and it was feared that they had gotten into the hands of the allies (whether they did or not is a matter of debate) and thus the plan had to be changed. Secondly and more importantly, a new and more daring plan was proposed. Eric Von Manstein, at the time Chief of Staff to general Gerd von Rundstedt , saw the flaws in the original plan and set out to make a new one. Manstein added what was called the “Sickle Stroke” which was the famous tank push through the Ardennes forest. Now when Manstein presented these plans to his superiors, they scoffed at the plans as “too risky” and “doomed to fail”, but Manstein wouldn't take no for an answer, and kept pushing for this new plan to get implemented. Franz Halder even went as far as giving Manstein a promotion just to get him to shut up; but even that didn't work. Manstein eventually used his friendship with Hitler's bodyguard Rudolf Schmundt to get a meeting with Hitler, who loved the plan. He adopted it almost immediately and passed it off as his own idea. Hitler's rapid adoption of the plan was also because he had grown tired of Halder and Brauchitsch, who he called “quibblers” and “cowards”.

The basic outline for the plan is this: Three German Army Groups, Army Groups A,B, and C. B will attack into Belgium and the Netherlands, drawing the allies into a fight. B will then cut through the Ardennes and rush for the Channel cutting off the armies in the Low Countries, finally, C will sit in front of the Maginot Line and just act as a deterrent.

Now this plan seems risky (and indeed it seemed very risky to the Germans), Fedor Von Bock, commander of Army Group B spoke against the plan saying:

You will be creeping by, ten miles from the Maginot Line, with the flank of your breakthrough and hope that the French will watch inertly! You are cramming the mass of the tank units together into the sparse roads of the Ardennes mountain country, as if there was no such thing as airpower! And you then hope to be able to lead an operation as far as the coast with an open southern flank 200 miles long, where stands the mass of the French Army

Bock and the rest didn't know it yet, but Manstein's plan was actually perfectly designed to take advantage of the weaknesses of France. The plan took advantage of the fact that the French and British were planning on rushing into Belgium at the first sign of German attack, the fact that France's airpower was in no way a match for Germany's, and the fact that the troops in the Maginot Line were static and would thus be unable to effectively attack the German flank.

The plan was labelled “Fall Gelb” or Case Yellow and was set for early May, eventually being pushed back to May 10th because weather concerns.

The Allied Plans:

Now if the German plan is daring, than the French plan was the exact opposite. The French held the most power in terms of decision making, despite the two countries being equal partners. The man in charge of the armies of France and Britain was a stuffy old man, named Maurice Gamelin. Gamelin developed two plans for dealing with the potential German invasion. The Dyle Plan and the Escaut Plan. Both called for taking up defensive positions along a major river, either the river Dyle or the river Scheldt (called the Escaut in French). In both scenarios the plan was to use the British Navy to blockade Germany while the French and British waited behind their defenses, building up their strength for a grand offensive that was to be launched in 1942-1943, when the allied militaries felt comfortable enough to launch one. Despite being unambitious, it was a sound plan at heart. Germany greatly relied on trade to keep its vital war industries afloat, and a full blockade would seriously hamper Germany's ability to make war. And France and Britain had no reason to suspect that Germany wouldn't try and repeat its strategy from World War One. This was to be France's ultimate undoing, it's plan was entirely predicated on the belief that Germany would do exactly what they did in WW1, there wasn't really any sort of contingency plan.

France would send the cream of their army into Belgium. There was the Second Army which was on the far right of the French Flank, their job was to stay near Sedan and guard part of the Meuse river, which was the only major water barrier standing between the Germans and the English Channel. The Ninth Army would guard the rest of the river.

The French First Army and the British Expeditionary Force, and any Belgians that survived the inital German assault, would Guard the river Dyle

Finally, the French Seventh Army would have the impossible job of trying to advance into the Netherlands and aid the Dutch army fighting.

This post will be finished in part two.

Edit: plane was not shot down, but got lost, thanks to /u/agrippa911 for correction.

The French (and the British) were defeated in the Battle for France because quite simply they came ready to fight WW I again. The Germans came in with style of warfare that handily defeated the Allies despite being inferior in numbers of things like tanks and aircraft. I'll give a rough list of several technologies and operational changes that caused this.

Radio: The Germans had them everywhere, each tank could at least receive orders and platoon commanders had a two-way set. This meant tanks could maneuver and fight with much greater precision. The Allies had fewer tanks with radios meaning platoon commanders had to often rely on hand signals, flags, or simply 'follow the leader'. Combine this with Allied tank design where the tank commander was also the gunner and you impair what were superior tanks (see below). German generals also used the radios which let them disconnect themselves from their HQ's and move to where they were needed.

Generalship: The Allies were prepared for a war at the pace of WW I. When the German forces arrived opposite Sedan in a sector only held by B class fortress divisions, the High Command didn't panic, they started routing reinforcements there confident that it would take the Germans a week to bring up the heavy artillery and ammunition stockpiles needed for any serious assault. Despite the performance of the dive bomber in Spain and Poland they never considered that the Germans might use airpower in place of artillery. Worse, Allied generalship was based on top-down orders whereas the Germans practiced auftragstaktik or mission-based orders, commanders were told what was expected of them and to accomplish it on their own initiative - go off plan if required. Whereas one French general wasted a valuable evening trying to obtain the written orders to counterattack (at a time when the German bridgehead was very vulnerable) despite having verbal authorization to attack. By the time he'd gotten his orders, then formed up his forces, enough German armour had crossed the river to defeat his attack.

Tanks: Contrary to popular belief the German tank force of 1940 was nowhere as capable as the one that invaded Russia. Of the 2,439 tanks used in France, 1,478 did not have anti-tank capability (e.g. Pz I or Pz II armed with MG's or 20mm autocannon). Of the remaining number, 278 were Pz IV's with the low-velocity 75mm gun which was only effective at short ranges (it was designed as an infantry support tank). That means only 683 tanks were armed with the 37mm high-velocity gun that was designed to take out tanks (Pz III, Pz 35(t), Pz 38(t) tanks). French tanks were more numerous and overall had better armour (e.g. French Char B2 or British Mk II). What made the German armour superior was first they all had good radios, longer range and speed (Allied tanks were often designed as 'infantry tanks', so operated at infantry pace with infantry range and thus required frequent refueling), but also layout. The Germans from the Pz III up had 3 man turrets - this meant the tank commander could concentrate on commanding his tank and leaving his gunner to shoot. Allied tanks tended to 1 or 2 man turrets which meant the commander had to shoot (and sometimes reload) and command his tank and maintain situational awareness. Simply put this gave the Germans a qualitative advantage despite a glaring quantitative advantage.

Aircraft: Again the Germans were outnumbered in theory. The Allies had more fighters than the Germans but used them badly. They were diluted and not used in strength, the key bridgeheads at Sedan weren't attacked until after the Germans put up huge numbers of AA batteries to defend them. Frieser thinks one reason for the poor performance of Allied air is that the French were planning on a long war (i.e. another WW I) so were stockpiling aircraft for the long-haul. The Germans wanted a short war and thus committed every single aircraft and thus achieved air superiority.

'Blitzkrieg' tactics: Regardless of who coined the term, it was a new strategy that was incredibly successful in France. Traditionally when an army broke through a defensive line, they'd start rolling up the flanks to widen the gap, consolidate while they brought up their artillery. The defenders would then counterattack to retake their position. 'Blitzkrieg' tactics threw out this playbook and just aimed at sowing confusion and fear by punching into the rear of the enemy with their armoured spearheads and leaving the following mechanized infantry and foot infantry divisions to worry about the vulnerable flanks - relying on speed for protection. The Allies would often hear of a breakthrough, then plan a new defensive line only to find the Germans had already reached it. The Panzer divisions caused massive amounts of fear, even if they weren't in the immediate vicinity, causing units to pull back for fear of being surrounded. These retreats (ordered and spontaneous) combined with bad communications, roads clogged with refugees, meant many Allied formations were combat ineffective not through enemy action but scattered or broken up.

Operational surprise: The Germans made a feint through the Low Countries and the allies fell for it completely. The Germans avoided any air attacks on the Allies as they advanced into Belgium to meet the advancing German forces (to spare France from fighting another war in its territory). This meant the Allies could advance quickly and with few interruptions, their best units to face the German distraction while the actual hammer advanced through the Ardennes towards Sedan and the planned breakthrough. German air then blew the everloving crap out of French defences and later Allied counterattacks.

Bad generalship: Quite simply the French had some shit leaders. Not all but unfortunately ones at key locations were bad to terrible. You had a commander of all Allied forces in one location, his headquarters was another location, the commander of Allied forces in the west in a third location. They didn't use radios instead often driving to the HQ to talk. And they hated each other.

For this specific place: France, at this specific time: 1940, the 'blitzkrieg' was an astounding success. But it would be hard to repeat, Russia didn't have the road network that allowed the Panzer divisions to move dispersed and consolidate quickly, it stretched on forever, and the Russians were much more tenacious. The Allies learned, slowly, painfully, but the Germans never found opponents as operationally unaware again. This is in someways a repeat (and reverse) of Napoleon destroying the Prussians at Jena - His Grande Armee destroyed the Prussian army built along the lines of Frederich the Great but which was unprepared for the speed and pace of Napoleon.

Sources: Len Deighton's Blitzkrieg, Karl-Heinz Frieser's The Blitzkrieg Legend

Nobody has mentioned the political climate in France. The military factors have been discussed many times by various authors. I especially like the analyses by Horne and Deighton. The Deighton book reads particularly well. In my experience the views over the last 50 years have shifted considerably and should be looked at carefully as far as military factors go and some ancient canards are repeated again and again. However that is not my point. The Political situation in the prewar Third Republic was very bad and it makes me think of the senseless polarisation we see in US society today. There were frequent disputes and deadlocks and much bitter acrimony in government. Both right and left were categorically opposed to each other and this was reflected at all levels French society. As one old French veteran told me "Nobody wanted to die for the Third Republic". Consequently civilian morale was poor and the memory of the bloodbath of 1914 was vivid. While the morale and performance of some of the first rate French units was good the overall malaise was felt through the armed forces. The Allies were simply overwhelmed by their own failings on so many levels it takes an entire book like Len Deighton's to even scratch the surface.

There is also a somewhat singular reason, which is simply that there wasn't a reserve force positioned to rapidly move to block any break through, and at the very least slow it down enough that the rest of the army could be mobilised against it.

Churchill documented this in his diaries, when he reports flying over to Paris to meet Reynaud and Gamelin. He describes walking through the courtyard where clerks were burning papers, and going up to look at the map of the German attack. According to him, his first question was 'Where is the strategic reserve?', which he then repeated in bad French as "Où est la masse de manoeuvre?". Gamelin replied 'Aucune', and Churchill at least claims that he knew the battle for France was lost at this point, and returned immediately to Britain.

Having a reserve force that can move up to at least slow down a break through is fairly elementary military tactics - so it's an interesting question as to why there wasn't one. The accepted version in Britain is that since the Maginot line was regarded as impregnable, there wasn't perceived to be any need for one, but it would be interesting to hear the French side of that.