French law recognises only the civil marriage. This must be performed by a French Civil Authority (officier de l'état civil), which includes the mayor (maire), his legally authorised replacement - the deputy mayor (adjoint) or a city councillor (conseiller municipal).
American diplomatic and consular officers do not have legal authority to perform marriages. Because of the French legal requirement that civil marriages take place in a French mairie (city hall), marriages CANNOT be performed within the Embassy or within an American Consular office in France.
Religious ceremonies are optional, have no legal status and may only be held after the civil ceremony has taken place (which can, but need not be, on the same day.)
