US immigration law allows dual citizenship as long as the other country also allows it, which is indeed the case for France. In terms of registering your children with the French authorities, you should consult with a French attorney to determine what age is appropriate for registering them.
Finally, the US government has published an excellent guide on this issue (from the US perspective), Citizenship Laws of the World, published by the Investigations Services of the US Office of Personnel Management (the entry for France appears on page 78):
http://www.opm.gov/extra/investigate/IS-01.pdf
Attorney Edward Weiner
http://www.immigration-aux-usa.com/