Assuming they can check EU wide, since france is party to treaties allowing mostly free migration throughout the EU to France and recognizes the authenticity of those EU nation states IDs for commerce and domicile in France.
Or you have a ID issued by France, and you'll use that.
Besides, heavily depends on how the verification services implement their checks. Whenever I (Spanish resident, Swedish citizen) end up having to do verification checks for some EU/Spanish service, they usually have more or less every type of ID I could have been using available.