Yes I think the Americans and the French take the P out of each other constantly, but since moving here I'm really struck by how alike we are.
I mean, most obviously there's the arrogance 
and the absolute conviction that one's own culture has everything you need. The reputation for rudeness abroad.
But there's also the gabbiness, for lack of a better word, the outpouring of small talk all the time, the willingness to tell complete strangers your life story. People are very direct, they will tell you what they think even if it's kind of rude.
I think there's similar attitudes toward health care, doctors give out pills more often, things like maternity are more medicalised, basically we're much more demanding of our doctors.
I think we're both more obsessed with food and restaurants. We tend to have bars, not pubs.
I should probably qualify by saying I'm east coast american, I lived in London, now I live in NW France -- so might think differently if I'd lived up north for example. But so far France reminds me much more of home than London did, which is weird.