I would have thought so, don't think it runs out, my friend was adopted but knew her birth mother was from new zealand. she was about 26 when she got her dual passport and she'd never even met her mum!
Actually I'm confused about this too. I have triple nationality (am chinese; was born in America but also got british resident passport) i guess it's ok?? hmmm
It depends on the particular country. A citizen of the UK is allowed to claim another simultaneous nationality, but I don't know about France. I know that to become a US citizen you have to renounce "any foreign power or potentate," requiring you to relinquish any previous citizenship.