France has always been a bit more independent and even outside NATO for a while; they kicked out all US forces from bases inside France and have a couple of former NATO air bases to play with as a result.
As for the deterrence, the French president does not have to ask permission from his own parliament to declare war on anyone, or to launch. Nor from anyone else. He can just give the order. In theory that's even more of a mandate than the US president.
France also still has an air deterrence capability with nuke-tipped almost-hypersonic cruise missiles (about 120 of them if I remember correctly), with a range of around 1000 km and flying very low at Mach 4, that can be fired from Mirage 2000 or Rafale multirole fighters, that can take off from French soil and refuel in flight. They call that 'raid nucléaire' and train for it, openly. The explicit goal of that is to be able to 'escalate to de-escalate' or go tit for tat if Russia uses a tactical nuke on a European battlefield. The UK has no tactical nuclear weapons anymore; NATO had a lot of them but destroyed/decommissioned them after the fall of the Iron Curtain. Even the US has only a very few left. Russia however still has a lot of them. Or at least they consider mid-range missiles with an 800 kiloton warhead that can wipe out a major city as 'tactical'... Their dogmas are different.
I don't think this is the place to get into 'who's stick is bigger' discussions; this is about bushcraft and at most, individual preparedness for disasters, of which war is just one amongst many possibilities. And in war there are only losers. I just wanted to set the facts straight, as I live in France under their largest low-flying training area (plus during the cold war I served as a noncom in the Dutch artillery corps, as an NBC specialist trained in determining fallout patterns and unit survivability calculations on a battlefield after the use of tactical nukes; and I also was watch commander on a site with nuclear ammunition, so let's say I have a particular interest in the subject...).
Better go back to tp, canned food in the pantry and splitting firewood for the living room stove during a blackout. ;-)