Yes, by the 100 year war, french monarchy was more powerful than the german one, but I think the memory of the nobles had not yet faded. The 100 year war was the crucible in which the french nation was really forged.
And I think it could have shattered in the forging. All it needs is a few more bad breaks for the french ( though they already had more than their share, OTL - you'd think ASB intervened - ). If you remove either Joan or Bertrand DuGesclin from the picture or have people convinced Charles VII is a bastard ( he himself wondered ), France will definitely fall to the english. Of course, after a few decades, the english King will move back to Rouen and england will be ruled from the continent, but that's another story..
About Burgundy, I think that, as late as Louis XI, it could have carved an indepedant kingdom out of what was northern France. If you remove Louis XI and make Charles a bit more diplomatic ( which are linked ), you'd achieve a Grand Duche d'occident which would cover the North of France, Belgium, the Luxemburg, Lorraine and Burgundy. From there, it can only grow.
And if you're willing to go a bit earlier than the 100 y war, the kingdom of Provence-Toulouse is a distinct possibility.
The last two don't destroy France as an entity, but this entity will have nothing to do with OTL.