After digesting a ton of French military doctrine, I think I'm ready for a gross generalization: The difference between the FR and US approach to war is the difference between Clausewitz and Jomini.

The influence of Jomini on the US Army has been well documented and argued about; his influence on FR is light, and for a bunch of reasons the FR Army (among them Foch, Aron, and, well, intellectual taste) is much more rooted in Clausewitz.

You can also see this in the work of Beaufre, Coutau-Bégarie, Desportes, and others. Besides all being into Clausewitz and having comparatively little time for Jomini, there's an intellectual compatibility at work. It suits French tastes. I don't know a better way of saying it.

Sigh, I'm really going to have to read Aron. He has a way of being indispensable.