> if you live in Paris and are offered a good job in London, and they help you deal with the visa stuff
Note that the freedom of movement in the EU means there isn't any "visa stuff" to deal with.
An EU citizen moving to the UK needs to fill in a form, to get a "National Insurance" number. The same would be required of a British citizen that didn't have one, for example if they'd been born and lived overseas before moving to the UK.
There are no other requirements that don't also apply to British / resident people moving within the UK.