Well, I have never heard of vows being used in ceremonies in France. The way my wedding happened, we showed up at city hall, signed the contract, the witnesses signed the contract, and then we went to celebrate. The only thing either of us said is "Oui", which is the French equivalent of "I do".
I don't know if vows are common in religious ceremonies, because I didn't have one and I've never been to one, but aside from that option, there just wasn't any room for us to make any vows. They did ask us before the ceremony started if we wanted to use rings, which we didn't, so maybe if we had they would have let us say something while giving each other our rings, but as it was we weren't supposed to speak at any other time, so I don't really understand that whole "keeping your vows" thing. The only thing we did is sign a contract and that's what I assume we should keep to.
We never promised each other monogamy either, although I guess he expected it.