So two things: First, Trump isn't a sane and rational actor, but there are sane and rational actors in the US federal government and especially Congress and the private sector (for example the media) that are doing the math on risk vs reward and coming to the conclusion that they should be backing him anyway. No man rules alone; if for example Raytheon or Amazon or General Motors thought that there would be serious consequences to their bottom line if Trump was allowed to continue, he'd have eaten a war powers resolution by now. Hitler wasn't rational, but you don't get Hitler without the industrialists and the industrialists backed Hitler because they were getting something out of the deal. Serious backlash from Europe would essentially unite the American capitalist class against Trump, with disastrous consequences for him.

Second, I partially took this into account, which is why I kept emphasizing actors outside the US whose consent mattered here. America can't project power into Iran without the cooperation of its allies in the Middle East who are much more rational and much more vulnerable to persuasion/coercion by Europe. Trade are obviously very important here (particularly but not exclusively to Israel), and Britain and France maintain important defense relations with several countries in the region. The Emirates for example are an important US ally on the region and I doubt they'd have allowed this to happen (at least on their own soil) if they feared that French arms would dry up. Nobody anywhere seems to have "Europe will hate/like me for this" as part of their calculations here and that's not the limit of the collective biggest economy in the world's influence.