France and the UK still have nuklear weapons, I would think the rest of the millitary would be more of a problem.

I would suspect both sides would not use nuklear weapons unless they get really desperate. So what is currently deturring Putin from attacking eastern europe is the thread of the reagular US millitary just kicking his ass and having no chance of gaining any land. But if it was just nato without the US he might gamble on them not using their nukes if he just takes, say northern Finnland, which he might think is feasable without US-troops.