The very different C3 reaction times came from very different doctrines. The French had their based in WWI, where battles were won by a systematical approach and where any deviation of the huge plan would mean your (massive) fire and (slow) movement would fuck each other up. Initiative was discouraged: "Don't think, just do what I told you - on time!". If the plan was allowed to fold out it would deliver crushing effect on the enemy, both in defense and in offense. And BTW the French army wasn't especially defensively minded. But it found itself far from ready for any offense in 1940, but probably would have undertaken one in 1941, if allowed to. Much like the mid to late 1918 offensives.
The Germans in contrast had refined and tuned the principles of Moltke the Older, where every man was expected to know the mission a couple of steps up, and also encouraged to use his own initiative and knowledge of the situation to find a way to the target.
So when the French 55th Division met the German main onslaught its commander drove around for 17 hours to find his superiors to get new orders, and in contrast Guderian actually disobeyed orders to slow down because he from closer to the frontline judged that he had an opportunity to be utilised.
Afterwards that was called "Blitzkrieg" but actually it wasn't a conscious doctrine before. Without the basic German principles of leaderships it would not have been possible however.
Blitzkrieg soon was blunted on the Eastern Front and I'll claim that the allied armies crushing Germany in late WWII used doctrines closer to the French in 1940 than the ditto of Germany in 1940.
There was a more pedestrian reason for this difference. The nazis threw funds at their military they did not have. The build up from 1935 was finance by serious deficit spending, accounting tricks, and looting the Austrian & Cezch economies. Resources the French leaders did not have acess to. The result was the German conscript inducted in 1936 or 2938 had about double the training of his French counterpart. The Depression left the French army with funds for a standard 18 months initial training for a conscript. Reduced from the 1920s standard of 24 months The Germans had a base of 24 months and increased it to 36 months. When the conscription classes of 1936 came due for discharge to the reserves a large portion were kept on active service until the war came.
The refresher training for the reservists was much the same. Far more weeks each year for the German soldier than for the French. & much the same for the NCOs & officers.
The outcome was the French could not progress past the initial stages of training during peace time. They could lay down a foundation of drill and basics, but the next levels where a leader could benefit from things like initiative were never reached. This defect was understood by the French generals, but any politician who proposed a military budget on the scale the nazis had was criticized for risking the economy.
The solution forced on the military leaders was to plan a intensive post mobilization training program. That had been implemented for the "Active" or first wave units a few weeks after mobilization, & to a lesser extent for the 'Series A' formations, the B series formations were not to start the full training program until the spring of 1940.
When you look at individual unit performance in the May-June campaign the first echelon units did fairly well. Even some of the second echelon units did ok too. ie: the 18th Inf Div fought Rommels 7th Pz Div for two days virtually alone & was withdrawing in good order when the promised support did not show up. It was the poorly trained formations like the 53rd, 55th, 61st, or the 71st that rapidly collapsed under pressure. All four of those occupied critical positions when Kleists three mechanized corps rushed them & all were left unsupported for a critical 24 hours due to the slow reaction time of the senior leaders. Better quality units like the 101st Fortress Div or the Morrocan Div of the 1st Army held their positions vs armored attacks, until ordered to retreat.