Fortunately or unfortunately depending on your perspective, Europe is too divided and too civilised to make that threat and probably at this point not strong enough from a military perspective to execute on it.
You left out one option in the the US's decision space: a surprise attack against Europe. I don't think the UK & France combined have enough nuclear warheads to cause an Extinction Level Event without US assistance. But still, if they think the destruction of human civilization is the correct position to take, might be best if we help extirpate them while they aren't sufficiently armed.
In a nuclear world you need to believe this (and your rivals need to know you 100% believe) or you won't survive to the next round of the game.