As far as I know there's a rather severe lack of nurses in France (as well as about everywhere in the western world I think) but I'm not sure your diploma will be recognized over here. And there's the work visa problem.
Since you're still a student, I guess the best way for you to come to France is to find an exchange program of some sort between your university and a French one. It will be all the easier to then get a work visa, learn the language and most importantly find out if you can actually stand the French and life over here.
Living on the coast would be nice indeed, but there are more work opportunities in the Paris area and universities tend to be more "international".
A few links:
American Hospital of Paris (your diploma might be good enough to work there)
American Hospital of Paris: Welcome to the American Hospital of Paris
Paris V university (biggest French medical sciences university):
(contact info for foreign students)
Paris VI university (many exchange programs with US universities)
UPMC - University Pierre and Marie CURIE - Sciences and Medicine - Paris
There are many more but I really think you should start by trying to find out whether your university can help you complete your PhD in a French university.
You could also try Montreal. The wages of nurses in Quebec are rather low compared to the rest of Canada, which means nurses trained in Quebec universities tend to flee the state once they get their diplomas and hospitals are in desperate need of nurses.
It's gonna be way easier for you to get a work visa (still a pain in the neck though) and have your degree recognized in Quebec compared to France. You'll be able to learn french and could try to move to France later (once you're totally fluent
Hope it helps a little !
Just ask if you have more specific questions or need help with anything like translating webpages only available in french, etc...