About the bit regarding you possibly commuting from Paris to London for work, I'm curious - how would that even work? Would you go through customs every morning/evening? Has anyone here done this?
Ahh I see what you mean, it would typically involve staying in a London hotel a few nights a week. Maybe traveling in on Monday mornings, and leaving on Friday afternoon.
I do have a British passport still, and I have a french residence permit, so in both directions it's fairly simple anyway (and the Eurostar is almost like taking a regular national train but it's a good 2-3 hours). Taking a flight is a bit more hassle and terrible for the environment (but cheaper).
About 20 years ago in London I worked with a guy who commuted from Greece(!) to London once a week. London salary, worked from home on Mondays, came in on Tuesday morning, budget London hotel on Wednesday and Thursday night, and back to a big house in Greece for the weekend.