The reason some people are querying that you allow US customers is FATCA. It isn't correct that you aren't subject to US regulations. Yes, obviously, in a reasonable and just world that would be the case, however the US is trying to change that as hard as possible as it appears that they are succeeding, FATCA implementation is proceeding at the moment - though it's not yet in force.

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Dave, as you're the one exposed to this stuff, please make super sure you have fully researched this topic. The US will force you to follow its rules whether you like it or not and the French government will not save you - this is not a paranoid hypothetical but a phenomenon that is already happening. Your best bet is to do what all other financial institutions are doing and deny access to "US persons"  (citizens, residents and people who have held a green card in the last 10 years, iirc). This doesn't exempt you from FATCA but it minimizes the amount of paperwork and reporting to the IRS you'll have to do.