It's a little simplistic to view France as the most powerful country on Continental Europe following WW1, yes they had emerged as a victor but at terrible cost with some 1.4 million Frenchmen losing their lives. This had a profound effect on the French people who obviously wanted to avoid another war of such cost and upon the French Military who looked for a way to win a war without incurring such loss. Interwar French military planning reflected these thoughts and as such proved inadequate in 1940.
One of the most important ideas that went into French thinking was the so called 'Verdun Factor'; the idea that even if the French were to enter a conflict with less than adequate equipment or preparation the inherently superior French soldiery would be able to provide France with a victory. Unfortunately parallel to this assumption of superiority was a moral quandary, was France prepared to suffer such terrible losses to deliver victory as they had in 1916? The answer was no, France's depleted population simply could not suffer such losses again and so another way to win had to be found. This led them to assess the trench warfare of WW1 and draw from it the conclusion that terrible losses could be avoided but only if they were to rely upon a network of fortifications that would act like the forts of Verdun and provide centres of resistance that would prove hugely difficult to capture. However unlike at Verdun when the forts had been neglected and so weakened this new line would not, it would be a continuous front from Switzerland to the Channel and thus nigh impenetrable.
The Maginot Line was born out of this thinking, in 1922 the French Army Commission concluded that a continuous line of defences would act as Frances shield, it would defend their territory (which with the recovery of Alsace and Lorraine no longer needed expanding) while simultaneously acting as a deterrent against German ambitions, they would surely not be willing to sacrifice so many lives attacking it. It was a direct reflection of their experiences in WW1 "We had been haunted by the tenacity of the German machine guns, and the impossibility in which we found ourselves of breaking the enemy front" wrote General Beaufre, France had not been involved in any of the more mobile campaigns in the East or Palestine and so had no people experienced in campaigns of manoeuvre.
However the Maginot Line was undermined by the French desire to involve the Belgians in their defence, in 1934 Petain (then Minister of War) said that in the event of a War the French plan was to "go into Belgium". At the time this made sense, France still enjoyed a huge superiority over Germany and it obviously seems preferable for a war to be fought as far from French soil as possible.
This kind of defensive thinking allowed the French army to ossify but it was not the only thing that undermined it. The so called 'hollow classes' caused by the drop in births during WW1 hugely depleted French manpower, the class of 1915 in Germany amounted to 464,000 men while in France it was merely 184,000. Additionally a French soldier received much lower pay than private workers and with the supreme national goal, revenge for 1870, achieved there was little reason for a professional to pursue a military career.
France was also undermined by the lack of funding made available for military spending, in 1936 (six years after the Maginot line was ordered) a fifth of spending was still on constructing and maintaining it. The French were also slow to adopt new technology, in 1924 the army decided to replace its infantry rifle, the new weapon was not selected until 1932 and by 1939 only a few hundred thousand had been issued. Mobile warfare was also not really ever accepted by the French Army, they took the approach of building a small number of prototype tanks each year but suspending mass production until a date when war seemed imminent which self-deception and appeasement delayed significantly this left them with a small number of tanks that were modern (depressingly the tanks they had, Somuas, were actually of very high quality) and a far greater number of obsolete relics.
Frances position would then go on to be significantly undermined by the announcement of Belgian neutrality in late 1936, this crippled their plan of rushing into Belgium and left them with a Maginot line that, although hugely strong, was simply too short and could not be extended through the industrialised north without incurring a tremendous cost which politicians in the Third Republic simply could not afford with the rising tide of anti-militarism in France.
I could go on about the political instability of France and how it undermined their ability to prepare effectively for war but I think I've set out a basic presentation of why Frances post war superiority is really only illusory and not reflective of their crippling instability and unpreparedness.
The whole point of the Maginot Line had been to safeguard eastern France, where much of France's industry, coal and iron was located; these territories had largely been captured by the Germans in 1914. More importantly though, it would force the Germans to once again go through Belgium, thus resulting in Germany being at war with Belgium, France AND Britain (and probably the Netherlands), all in one fell swoop. The French and British armies being better equipped and supported by airpower, it was expected that the Allies would then be able to destroy the Germans in detail, and then go on the offensive with armoured forces (probably by 1941).
The only problem with this plan, was that when the Germans DID attack, they didn't attack as the Allies had believed they would. In January 1940, a German officer had crash landed in Belgium, carrying the German plans for the invasion of France and the Low Countries, that seemed to confirm Anglo-French assumptions. However, this prompted the Germans to radically change their plan: in a new offensive plan developed by General Erich von Manstein, the Germans would place almost ALL of their Panzer and Motorized Infantry Divisions under one command, Gruppe von Kleist, which would advance through the Ardennes Forest. The Ardennes was by far the weakest point of the Allied lines, but this was because the terrain, very hilly and mountainous, with only a few good roads, which could easily be blocked at key crossroads or attacked with aircraft, was NOT the kind of terrain through which one would send ALL of your tanks and motorized troops, unless you were mentally ill/reckless/had a serious death wish. Many generals, Franz Halder the head of the OKW (Armed Forces High Command) especially, were horrified, but the Fuhrer thought it was daring, and Hitler was nothing if not an avid gambler (especially with men's' lives).
The Germans ultimately got UNBELIEVABLY lucky. Lucky that the British and French never detected the advance through the Ardennes; lucky that the Luftwaffe gained a good degree of air superiority from day one, despite Polish warnings that the Luftwaffe would target Allied airfields; lucky that when they emerged from the Ardennes, which quickly became traffic-jam CITY, the only barrier in the way, the River Meuse, was guarded lightly and by second hand troops; lucky, most of all, that the Allies ultimate plan, to hold the Maginot Line along with the so-called 'Dyle Line', and send troops to help the Dutch, left them with no mobile reserve; if they had possessed such a reserve, potentially the French 7th Army if it hadn't been sent to help the Dutch, the break through would have been nowhere near as successful as it was.
Finally, the Germans were aided by other factors, most notably a complete failure of the French High Command, and of Allied communications. Paul Gamelin, the French overall commander was completely out of touch with his forces, while communications eventually became a shambles as the Germans interrupted communications between the Armies. by June, 1940 French morale had all but plummeted, and with most of the French Army's best troops trapped in the low countries, or bogged down in heavy fighting along the Maginot Line, defeat was really only a matter of time.
Ultimately, the Germans 'luckily' 'crushed' the French Military/Frances heavily fortified border. Wherever the French and British could resist effectively, it showed, and the Germans suffered considerable losses. The fighting to clear the Maginot line was especially arduous, requiring many forts to simply be destroyed by explosives, trapping their garrisons inside, because the Germans simply couldn't dislodge them without incurring heavy losses. The campaign also exposed how insufficient the armour and armament of German tanks were, compared to those of the Anglo-French, something that was not really remedied until after Barbarossa, when the T-34 and KV-1/2 were encountered. The German tanks had benefitted from better communications, better leadership, greater maneuverability, and from better allocation of vehicles: tanks were concentrated in Panzer (armoured) Divisions, instead of being spread between Brigades and divisional battalions as they were under the British and French, though this had begun to change by summer 1940, albeit too little too late.
In fact, the French and British combined had MORE tanks than the Germans, it was how they were UTILIZED, again, that made the difference. The French had actually also spent a large amount of money outside of building the Maginot Line, and had accumulated formidable amounts of tanks, and a large and growing air force. The only problem was that French politics were chaotic, something really symptomatic of the French Third Republic in general. Funding was sporadic based on who was in control, production was made difficult by labour issues, and modernization took place in jumps and starts. Furthermore, the Germans had also been building considerable fortifications in the 30's, the Siegfried Line in the west, and the Ostwall in Pomerania and Silesia.
This post is, without a doubt, THE most comprehensive account of France's fall in /r/AskHistorians, highly recommended and it should answer your question directly.
Does anyone know of a good primary source from a French soldier during the Battle of France, in English or French? An account by someone who had first-hand experience of all the deficiencies that plagued the French effort?