Expanded from an earlier answer of mine that covers the meat of the question.

The situation in 1940 was also a bit more complicated than the Germans going around a fortification or resurrecting the Schlieffen Plan. The Maginot Line in many ways performed as expected in 1940. The Germans were unable to break the line outside of a few areas, and even here these were costly attacks that achieved more in terms of propaganda than actual military results. The Line itself was not all that expensive in the bigger picture of French defense outlays and it did prevent a German thrust into central France. Fall Gleb managed to stumble onto a fracture point in Franco-Belgian defense and exploited it to the utmost.

One of the popular complaints about French military policy, both in the immediate aftermath of 1940 and continuing in the postwar, was that Belgium's adherence to neutrality hampered the overall defense of the West against Germany. Alistair Horne in his famous To Lose a Battle described Belgian policy as akin to the nursery the rhyme Three Little Pigs in which Belgian intransigence ensured that "in one stroke [France's] Maginot Line strategy lay in fragments." Horne and other commentators would assert that the Maginot Line should have been extended in light of Belgium's insistence that it was a neutral, and as such could not have belligerents stationed on its territory. Such critiques though miss key elements both of Franco-Belgian grand strategy and ignore some of the problems inherent in extending the Maginot Line into this region.

While Belgium's public face was that of a neutral, its defense policy was definitely pro-French and geared towards cooperation with Paris. There were significant war plans and cooperation between the two countries' military establishment and both conceptualized many of the same problems. The critique that the Maginot Line should have extended through the frontier border misses the key fact that French strategic thought saw the Belgian frontier with Germany as the proxy extension of the Maginot. One 1932 French General Staff document noted that:

Belgium, by its geographic situation, constitutes the glacis of our northern region. Besides, it considers France as its natural ally. In case of German aggression, it will very probably request our support and its forces would cover, at the same time as Belgian territory, the meeting of the French armies destined to fight at their side.

This conceptualization of Belgium as a glacis meant that the French general staff encouraged the Belgians to fortify the Albert Canal and Dyle River regions. While these fortifications were not on the scale of the Maginot defenses, they were not supposed to reach this level of fortification. Instead, they were intended to delay a German advance long enough for a link up of French and Belgian troops that would destroy the invading Germans in a methodical battle, hopefully along the flat plains around Gembloux.

This strategic plan made French fortifications along the Belgian border somewhat superfluous. The whole idea of French planning itself was predicated on pushing Germany to invade Belgium and then being delayed by geography and fortifications long enough for French forces to defeat them in a set-piece battle. The Maginot Line itself discouraged an alternate, direct thrust into France, leaving Belgium the only real option for German planners. There was some thought given by French and Belgian planners in the 1930s to fortifying Arlon region of the Ardennnes as a contingency plan, but not much came of it. Belgium was unwilling to cover the costs of fortifying this region, and even when the French offered to pay for it in 1934, the Belgian Foreign Minister rejected it. The official rationale was that this would have been too flagrant of a violation of Belgian neutrality, especially for a peripheral area.

Although Belgium's rejection of the French offer seems foolish in hindsight, there were solid reasons for it at the time. Belgium's defense appropriations were already quite high and the Belgian government was having trouble paying for the fortifications on the German frontier. The Ardennes region itself was rather poorly suited for fortifications, being quite hilly and wet. This was one of the reasons too why the French did not seriously consider extending their own Maginot fortifications into this region. Costs of the existing Line were large and the overall sentiment in the French high command and government was such man-made fortifications would be superfluous in light of the region's unsuitability for mobile warfare. Phillipe Petain was on record saying that the Ardennes was impenetrable and Gamelin described the Meuse River as "Europe's best tank obstacle." This however does not mean that the French military completely ruled out any attack through the Ardennes. The French high command estimated that because of the roads and geography, a German attack would likely take nine days to clear the forest and two weeks to reach the Meuse. If a German attack were to materialize in this sector, then the French high command believed they would have ample time to organize an efficient counterattack. In this scenario, the forest and the Ardennes's terrain were expected to act as fortifications that would delay a German advance like the Dyle fortifications.

The German thrust in the region would prove this expectation to be woefully optimistic. Fall Gelb's panzer and mechanized forces proceeded far quicker than most of the French high command expected, sixty hours to clear the Ardennes and a day to reach the Meuse. There were many voices within the French military that challenged this complacent attitude to the Ardennes in the 1930s. One of the local commanders, Colonel Bourguignon, conducted an exercise that demonstrated tanks could operate far easier within the Ardennes than French conventional wisdom dictated. In 1938, the commander of the French Second Army, General Andre Pretelat, conducted a map exercise that closely resembled Fall Gelb's thrust. Pretelat's estimates of a German attack's speed were only off by a mere three hours. Gamelin accused Pretelat of pessimism and the exercise was kept secret.

It is also worth noting that some in the German high command shared the sentiments of Gamelin. Halder too thought the Meuse could only be reached in nine days at the earliest. Throughout Fall Gelb the German command was torn between two loose factions, the traditionalists and modernizers. The former feared that overextending panzers without proper infantry support would open up the German thrust to the dangers of an organized counterattack. The modernizers like Guderian favored a Bewegungskrieg (war of movement) and thought that mechanized forces and airpower would make up for the lack of infantry support. Lest we fall into the trap of at type of Calvinist historicism (modernizers are the elect and traditionalist the damned), remember that at various points Fall Gelb took extraordinary risks that could have been disastrous had the Allied forces acted more proactively. At the Battle of Sedan, the official Bundeswehr study of the campaign asserts that the local French commander had everything he needed to stop Guderian's thrust except an order to do so.

The German's key advantages were both concentration of forces and operational flexibility. Although the Allies had numerical superiority and a rough technical parity in the air (there's a lot of hair splitting in many of the comments as to how superior one force was over the other), the larger and arguably more important point is that German airpower had effected a numerical superiority over the schwerpunkt. This made it much harder for the French to suddenly shift their airpower over the Ardennes. The Luftwaffe enjoyed a relative proximity to the main bases and were not operating at a distance. German concentration was not limited just in airpower, the I Flak Corps was in full force and prevented Allied airpower from exploiting the gaps in the Luftwaffe air umbrella. Furthermore, the Flak arm proved instrumental in its dual use against French fortifications and Allied tanks. Rommel famously stopped the Cambrai counterattack with his mobile flak units. As Fall Gelb developed, German airpower lost these advantages in concentration of force and proximity to German airfields, and that is when losses started to creep upwards.

Overall, Fall Gelb was successful because it took a calculated risk that payed off handsomely. The Germans offensive played to their strengths, but they were aided considerably by the sluggard French high command. Fortifications in the Ardennes might have helped, or even stopped the German thrust, but that obscures the fact that the Ardennes thrust walked a knife's edge between success and catastrophe even without fortifications and facing reserve troops.

Sources

Citino, Robert Michael. Death of the Wehrmacht: The German Campaigns of 1942. Lawrence: University Press of Kansas, 2007.

Dildy, Doug, and Peter Dennis. Fall Gelb 1940 (1): Panzer Breakthrough in the West. Oxford: Osprey, 2014. 2014.

Epstein, Jonathan A. Belgium's Dilemma The Formation of the Belgian Defense Policy, 1932-1940. Leiden: Brill, 2014.

Frieser, Karl-Heinz, and John T. Greenwood. The Blitzkrieg legend: the 1940 campaign in the West. Annapolis, Md: Naval Institute Press, 2005.

Nord, Philip G. France 1940: Defending the Republic. New Haven: Yale University Press, 2015.

Part 1 of 2

Yeah, I know the memes you are referring to u/manorbros, you often see things like "The Germans just went around the Maginot Line" and "The French used tanks as infantry support, not in concentrated armoured units". As you might expect, the reality of the situation was not as black and white, and a lot of these myths or oversimplifications started with historians writing in the 1950s and 1960s, and with German generals like Halder and Guderian who wrote rather self serving memoirs after the war. These have stuck around in pop history ever since even as the historiography concerning the period has moved on. To give you an idea on what has been written on the genesis of the defeat in 1940, authors such as Robert Doughty point to army doctrine, Ronald Powalski points out the rigidity of the French command structure, Ernest May looks to memories of WW1 and fear of bloodshed, and Alistair Horne points to political divisions and divisions in the army between classes (such as those between officers and men). However no one, with the possible exception of Eugenia Kiesling, has tried to combine all of these elements into a coherent narrative. For what it's worth, i'd highly recommend her book Arming Against Hitler: France and the Limits of Military Planning.

Maginot Line

First, let's address the Maginot Line. The French examined the idea of extending the Maginot Line along the Belgian border in some detail but rejected the idea, partly for political reasons to do with Belgian neutrality but also for some sound strategic reasons:

(A) The terrain on the Franco-Belgian border was completely unsuited to defence and is largely open fields intersected by rivers making it exceedingly difficult to fortify. It also has a high water table meaning it was impractical to build underground, and as the area along the Franco-Belgian border is heavily industrialised, it would have caused a lot of disruption to vital industry had they begun building forts in the area.

(B) The main industrial and population centres of France are in the North-East of the country which presents a significant tactical problem. Here is a link showing a map of France, within the red circle lies 50% of France's GDP today: https://imgur.com/a/92gJx Back in 1940 industry was even more concentrated in the North-East, and as Doughty lays out early in Seeds of Disaster and Breaking Point: Sedan, ninety percent of France's cloth and woolen industry was north of the Seine as were the majority of the chemical industry, 100% of the automobile factories and 100% of the aircraft industry. As noted before, lots of population lived near these industrial centers and as such they could not be lightly surrendered to the enemy. Aside from industry, this region also contained lots of natural resources, 75% of France's coal came from here and all of France's iron ore came from the Briey-Longwy basin in Lorraine. The French were aware they needed to move the battle away from this area if they were to have any chance in holding until their allies could come to their aid.

(C) Holding until here allies came to her aid was the most viable strategy for France. They knew in a 1 on 1 fight with Germany, they would be in serious trouble as Germany had more population and industry than France did. France actually mobilised 300,000 less soldiers in 1940 than in 1914. Fortifying and sitting on the border meant the battle would occur in the most industrially valuable parts of France, and France would not be able to hold until help came. So the French plan was to push the front forward and fight the Germans in Belgian, not French territory, along the Dyle river (in what was called Plan D or the Dyle Plan).

(D) The French command was fully aware that any "line", attacked with enough strength, could be breached. Gamelin (French Commander in Chief) wrote in 1935, “from 1915… whenever the necessary means were judiciously employed, one always broke a front.” (Kielsing, Arming Against Hitler) When the Maginot Line was completed in 1935 it was impenetrable to the German army of the day but the French had no illusions about the sanctity of fortifications. If they had extended the line along the Belgian border the forts in exposed areas (fields and rivers remember) would have been broken quickly by heavy artillery, bombers etc. and the French high command knew this in part due to what had happened to the Belgian forts at Liege in 1914 and their own experiences with the forts surrounding Verdun in 1916.

(E) Defending the border would present a significantly longer front to defend than moving into Belgium and defending along the Dyle river. This was a problem due to what I mentioned concerning the number of men that France could field. Besides a shorter front, the French needed the extra 22 divisions of the Belgian Army plus whatever the Dutch could field to even out the manpower imbalance.

The Maginot Line was a force multiplier in today's parlance, designed to screen the border regions, allow the army to mobilise and funnel the Germans through Belgium where the French army's mobile elements could manoeuvre and counter the German advance. It was a practical and useful response to the strategic challenges faced by France at the time. It actually allowed France to garrison the Franco-German border with only 15% of its total number of soldiers.

Mobile Warfare

Now let's move on to the way the French army operated in the field. Perhaps the most pervasive criticism of the French in 1940 was that they failed to understand the changes that had taken place in warfare since WW1, chiefly that they hadn't embraced combined arms and mobile warfare. However as Kiesling shows, the French military was well aware of new theories on mobile warfare. A resurgent Germany forced on France the problem of translating strategic ideas into a set of specific actions. However between theory and practice there were political, social and economic obstacles that caused a number of problems. France was limited by her political institutions, history and other factors, as were other powers.

It's worth noting that in 1940 France had:

7 x Motorised Infantry Divisions

5 x Mechanised Cavalry Divisions

4 x DCr or Division Cuirassée de Réserve (a heavy armoured division, light on infantry)

3 x DLM or Division Légère Mécanique (a well balanced medium armoured division including motorised infantry, artillery, AA and anti-tank sections)

In addition to this there were indeed tanks designed for infantry support, these consisted of 30 independent tank battalions generally deployed in regiments of two battalions each and assigned to army and corps reserve formations.

The DCr and DLMs were the functional equivalent of the German Panzer divisions, that is the French envisaged using these in the breakthrough phase of battle. France had 7 of these divisions to the 10 Panzer divisions Germany had. When you account for the differences in population and the relative size of the two armies, they were therefore roughly equal in terms of mechanisation.