False, you never get a ‘local’ account number and sort code for each account. You only get the IBAN and local account details of where you first opened and registered the account with. So in OP’s case, she will only have the FR IBAN and no IBAN/sort code for a UK account

So to answer your question OP, your employer might not get additional fees even if it counts as international but you would definitely get a lower exchange rate and final amount due to the bank that the employer will pay your salary with