Paris,Yerevan, and Baku

https://eurasianet.org/armenia-azerbaijan-macron-stirring-things-up-in-the-caucasus

Baku is in a fairly cozy relationship with Washington and thus if the Americans don't want to see Macron make this move, you can be sure the Azeri government will speak out and condemn French overtures.

Additionally, Azerbaijan does not want to draw Russia back into Transcaucasia, especially in an interventionist role which is likely if NATO becomes directly involved in Ukraine. Regardless of what happens there, Moscow will have nothing to lose in moving to break any pro-NATO resistance in Georgia and Armenia. Such a move will create difficulties for Azerbaijan and potentially bring a larger war to their region.

Armenia is looking for allies and Paris has long been antagonistic to Türkiye - and it's hard to separate Ankara from Azerbaijan. They are not one and the same but the ties between the two countries are substantial. Even Erdogan's falling out with Washington hasn't changed this.

And as the article suggests, there's currently a gap, a vacuum created with the recent Armenia-Azerbaijan War over Nagorno-Karabakh. Russia's traditional role in Armenia has been called into question and the relationship is at a nadir. Macron is seeking to capitalize on this opportunity - once again France is fulfilling that traditional role of moving into the gaps left and created by Washington. Usually it frustrates the Americans and probably is now to some degree. And yet if Armenia can be pulled out of the Russian sphere without a direct conflict, many in the United States will chalk it up as a win.

No matter which way this goes, it's effectively a loss for Moscow. And at this point in a time a serious intervention is probably not being considered. If need be, Moscow will respond, but it would have to be something that involves a direct threat - such as a bid for Armenia to join NATO. That's a long ways off. Nevertheless Moscow will certainly flood Armenia with money and work for a favourable political solution.