The answer that has currently been given seems to be pretty good on the technical differences between WW1 and WW2 but I would like to detail the differences in strategy, doctrine and morale that led to the swift French defeat in 1940.

The German plan of WW1 envisioned attacking in a wide right hook across Belgium into France that would encircle Paris and swiftly defeat the French. However, by 1914 this had been diluted with a large number of troops being shifted down to protect the German France border, where the Germans expected the French to attack them. Additionally the Germans shifted elements of their invasion force east to counter the Russian invasion of East Prussia. In 1940 the Germans launched an armoured attack through the Ardennes and then pushed to the coast cutting off the BEF and French First Army.This had not been considered possible by the Allies in their pre war planning. The tremendous success of this attack shocked the British, French and Germans who had not expected the level of success they achieved. So the plans were not identical and this was crucial in the success of the latter.

In 1914 the Germans were operating away from their supply bases as soon as they entered Belgium, this was the same in 1940 and the majority of the German Army was not mechanised and moved at the same pace as the armies of 1914. However the critical difference is that the Germans did possess Panzer Divisions that were capable of moving into France much swifter than the Armies of 1914, though they too suffered from reaching the end of their supply lines and this was a significant factor in how the British were able to evacuate the BEF at Dunkirk.

Tanks had been considered important by almost all Pre WW2 armies but the Germans had found a much better way of using them concentrating them in Armoured Divisions and then using these to spearhead a breakthrough supported by air cover that replaced slower moving artillery as fire support. This was different from the Allies who mainly envisioned Tanks being used in support of infantry attacks and thus deployed them in smaller groups. The French SOMUA S 35 was superior to the Panzer III but was not deployed effectively, The Russians would go on to have the same problem in 1941 with the T 34 and KV 1.

But, in my opinion, by far the most important reason for understanding the different result of fairly similar plans is the huge decline in morale the French suffered following the initial German attacks in 1940. It is worth remembering that WW1 had a profound affect on the French people, they suffered horrendous casualties and did not possess anywhere near the same levels of national jingoism that they had in 1914. After the Germans broke thorough in the Ardennes and Sedan there likely was a real opportunity for the French to counterattack when the German Divisions were almost totally out of supplies and over extended but they did not capitalize well on this, their will to fight almost totally broken. This was present at both high command, where the French repeatedly demanded that the British commit a larger number of Fighter planes and repeatedly sent messages saying that the Battle was completely lost without them, and at the enlisted level, the majority of the 111,172 French troops evacuated at Dunkirk subsequently chose to return to France rather than join the Free French with De Gaulle.

I think its important not to blame the French for their failure in 1940, no one expected the Germans to do as well as they did and the opportunity to counterattack, if it existed at all, was very brief and understandably not utilized well.

Sources; France 1940: To lose a battle, Alistair Horne

Finest Years, Max Hastings

1914-1918 The History of the First World War, David Stevenson

The World Crisis 1911-1918 Volume 1, Winston Churchill