Wait... You think Trump is president of the UK and France now?
I'm not sure where you're going with that but I'll humour you anyway.
As long as I've been old enough to notice, the UK has usually done whatever the US wants it to, to varying extents.
Right now, May is so far up Trump's arse the only thing still visible are the soles of her fancy shoes.
So, when it comes to bombing people, yes, Trump has a substantial degree of control over the UK.
However, this isn't unique to Trump, not even close, and the subservient bum-licking was even worse during the Dubya-Blair bromance.
The hierarchy in the US-UK relationship usually manifests itself when the US attacks some country and the UK then joins in, simultaneously issuing ludicrously grand-standy statements that attempt to give the impression that the UK would attack another country "for the common good" and without the blessing of the US, far less at their request.
I'm not sure who these statements are targeted towards as I've never met anyone who is taken in by them. Not even people who agree with the bombing.
As for France, someone else can humour you on that one.
I'd simply add that when they're not cheese-eating, freedom-fry-howking surender monkeys, they're apparently full of bomb-droppy-murdery wisdom.