FIA and ACO have a joint interest in GTs, but differ sometimes in the regulations. The MC12 is FIA homologated but refused by ACO.
ALMS follows most of the ACO rules, with the lighter LMP2s as a notable exception. LeMans is a registered trademark, so if ALMS wants to use that name somehow, they have to listen quite closely to what the French have to say. And let's face it, for many teams participating in the Le Mans 24 hours is there reason for being. (again with some notable exceptions...)