it seems strange that France would make such a move.
It doesn't seem at all that strange to me. France has traditionally positioned itself as protector of Christians in the Middle East (e.g. Lebanon) and sometimes in the Caucasus too. (Yes, that's sometimes seen at odds with the secular nature of the French state.)
More recently, Armenia's government has been unhappy with their arrangement with Russia--and this went both ways. Armenia in particular was unhappy with effectiveness of Russian weapons they've got, in countering Azerbaijan's arsenal, which includes some more modern weapons provided by Turkey and Israel.
In the 2020 Second Karabakh War Armenia's air defense turned out to be woefully unprepared for the onslaught of Turkish and Israeli-made drones used by its adversary Azerbaijan.
So Armenia has been looking to upgrade, qualitatively. And they've cut down their participation in the Russia-led CSTO to bare minimum, while pursuing more ties with NATO and the EU.
If you really want some French statement:
"We are the first NATO country to have an open and confident cooperation in the field of defense with Armenia. And that's a signal to the regional environment, of course, but it's also a signal to our NATO partners," France's ambassador to Armenia, Olivier Decottignies said in an interview with CivilNet on November 2.
One other thing worth mentioning perhaps is that France, unlike some other European countries, needs/gets no gas from Azerbaijan, as far as I know. They sometimes even chide other European for that...
"Is buying gas from Baku any less reprehensible than buying it from Moscow?" asked François-Xavier Bellamy, one of the leaders of the Les Républicains (French right-wing) party and a supporter of Armenia [...]
(An irony is though that Frace-based multinational TotalEnergies is involved in exploiting the Azerbaijani gas fields though, even if the customers for that gas are not French.) France has arrangements with the Maghreb countries etc. And in fact, even a bit of conflict with (Azerbaijan's ally) Turkey over the gas fields off Libya, via the competing Libyan factions that claim to be the government of that country.
French animosity with Azerbaijan goes both ways, of course. France is often attacked by Azerbaijani TV stations and politicians for colonialism etc.