[naraht]

OK. Let's see if I can boil it down.

In the USA,
Step 1 a marriage license is obtained from the Civil Authorities. Note, in some states this doesn't have to be done in person. If they fit the criteria in the law, it is issued, and the couple can proceed to step 2.
Step 2 *either*
A. A designated representative of the juristiction (Justice of the Peace, Town Clerk, Judge, Supreme Court Justice (yes they are allowed) etc) performs the marriage, signs the marriage certificate and files it. Congratulations.
*OR*
B. A Religious officiant who has been vested with the right to perform a marriage (that's where the phrase "By the power vested in me by the state of Iowa...") performs the marriage, signs the marriage certificate and arranges for it to be sent back to the juristiction that files it. Congratulations.

In France, 2B is not a choice. Whatever a Catholic Priest, Jewish Rabbi or whoeever else religious does in regards to a marriage is *completely* irrelevant in regards to French Law.

BTW, the rules in various states for getting the power vested in a person to perform marriages vary greatly. Some states you just have to ask and pay a small ($25ish) fee. Some states you have to at least come up with a Church name, that's where those advertisements for getting the right to marry. For *certain* states, you send the mail-order church a fee, they send a document saying you are a minister of that church and you can get the right to marry. Consult your local laws...