I was going to entertain the idea but no, I don't think they would. I think that they would use an obvious loophole which is that it is primarily the business of France and Germany since these countries are EU members and that they share that territory. Whether the US do anything would depend on what France and Germany do, want to do and more importantly can offer.
I'm very cynical on that topic because you just have to look at the Turkey, Cyprus and Greece conflict in the last 3-4 years, almost everyone acts as if nothing is happening and yes Turkey are a member of NATO but it tells you that the way they take decisions isn't based on what is right or wrong but what suits them, by them I'm talking about any nation not just the US.
Even the powerful nations stay away from actual conflict and tensions as much as they can and they will use any argument to do so. They have no issue with posturing and poking though.