Moving from France to the UK

Ask Mrs May! This is quite unknown.
The current position however is the UK will guarantee a settled status for newcomers moving from an EU country to the UK, if they settle before the "cutoff" date which possibly is March 19. (note: in practice, this means you will have to be able to demonstrate this)
Secondly, that predefined settled status will be very different from the current permanent residency, meaning newcomers who are granted the status after a few years are unlikely to ever get residency nor citizenship - again Mrs May or the Home Office to clarify!
You can keep informed of the details by going to the Home Office website and registering your interest. You then receive regular updates on the subject. I'm not concerned as I'm British, but something to note is their newsletters can't be of the greatest accuracy since the points of debate have been moved to all directions for the last 18 months....