The question of prohibited calibres/cartridges in France seems to arise quite frequently. Hopefully this answers it, but note that this is not legal advice.
It would appear that rifles chambered for the following cartridges, as well as ammunition, are prohibited:
.30-06 / 7,62X63
.308 Winchester / 7,62 NATO
8X57JS / 8 mm Mauser / .315 Mauser
It would also appear that the following ammunition is prohibited (not the rifles themselves):
6,5X54 Mannlicher Schoenauer
6,5 Krag / 6,5X55
I believe that in addition, there are handgun calibres/cartridges that are also prohibited as well as certain types of rifle action.
I hope that is of some help, but please check the legal position for yourselves before travelling.