My sense is that they won't.
The French believe they should be the world's leaders (no kidding, they really do) and they're going to be a pain in our ass in perpetuity.
I saw a really interesting segment on, maybe it was Gibson on Fox, can't be sure now, possibly could have been on msnbc, but it was earlier on Wed evening. The guest was Michael Cherkasky, a terrorism and security expert, who said (paraphrasing only slightly) "Since the end of the Cold War, France has been our principal enemy."
I thought it pretty amazing that it was spelled out as boldly as it was, and can only suppose that our govt to some degree believes the same.