The French started building nukes after Suez to keep their standing in the world, not as a deterrent but so they could keep acting like a big boy.
Not really. They considered (unlike the UK) that French vital interests couldn't be guaranteed by the sole US alliance, which of course was even more pregant in French doctrine after De Gaulle came back to power.
Note that the French nuclear force has two distinctive features :
-it is a "arme tous-azimuts", which implies that nuclear arsenal might be directed at
any immediate threat for the country's vital interests (primarily the USSR, but technically, it could be as well China or the US)
-it is supposed to be fired once French territory is entered, with no warning strike. The idea, as De Gaulle told, was that "even if the Russians may kill 800 million Frenchmen -assuming there would be 800 million French people-, they'd hesitate to cross the Rhine if we were able to kill 80 million Russians."
This said, any other option that a major conventional war with imminent invasion of French metropolitan territory belongs to the realm of ASB. As for operation vulture, it's not as if the US never considered using nukes in a contemporary war is some not-so-distant peninsula...