In terms of American remakes of French films,
I think most of them are financially more successful (from the batch made in
the 1980s
and 1990s). Jennifer Forrest and Leonard Koos
have a good book about remakes called:
Dead Ringers: The Remake in Theory and Practice
Also see Lucy Mazdon's
Encore Hollywood: Remaking French Cinema
and Nancy A. Durham's book Double Takes:
Culture and Gender in French Films and their
American Remakes
Both of those books include a lot of material
about the economic and aesthetic comparison between French/American remakes.
American remakes of American films are another
whole topic. Andrew Horton and Stuart
McDougal edited a volume called
Play it Again, Sam: Retakes on Remakes that
deals specifically with this issue.