Well, of course the claim is absurd. The only thing that could destroy such a big area would be a dinosaur killer asteroid, which would, of course, cause mass extinction all over the planet, including possibly even H. sapiens.
But a large yield nuclear device detonated in France could make large areas of the country uninhabitable for quite a long time, as well, as spreading radioactive fallout for tens of thousands of square miles.
Now, of course, striking a NATO country would inevitably lead to retaliation. Both France and the US have nuclear arsenals, and while France's is relatively small, it is certainly enough to do some significant harm to Russia, and the US, of course, has more than enough firepower at its disposal to do some nasty harm. Naturally this would lead to a near-universal conflagration which would likely lead to major geopolitical instability.
Which is why, of course, neither Russia or the United States are going to be lobbing nukes at each other or at each other's allies, and why, even if Clinton were to institute a no-fly zone in Syria, and Russian or American jets got into a firefight, while it would certainly lead to some pretty angry outbursts, isn't going to see World War 3.
We've been down this road before. The West and Russia spent forty years staring each other down, with some pretty close near misses like the Cuban Missile Crisis, and there was no WWIII. The idea that Russia, so much weaker in every respect than the USSR, represents that kind of threat is absurd. The USSR had some ability at force projection, whereas for Russia, Syria is just about the outer limit. Whether the Russians like it or not, the US has largely downgraded it to regional power, and its chief long-term concerns are now China.