In this case most likely OP will not be 'employed', they will be self employed and working through a business to business relationship with the US company. In that case they will need to pay their own social security contributions in France, where as if you are employed it is paid by the employer/comes out of your gross salary.

To be 'employed' the US company would need to setup a legal entity in France, and ensure they are compliant with all French labour laws, which doesn't really make sense for them to do for a single person.