These are all ways of transferring into â‚¬â‚¬â‚¬s from Â£Â£Â£s in a bank account. If you want to transfer â‚¬â‚¬â‚¬ notes-and-coin from the UK, there is a much shorter answer: don't even think about it. I started off trying to explain why, but didn't have the energy: you have the right to waste modest amounts of money doing thing you haven't bothered to understand.
I will apologise for this before I get kicked off the forum. I can only say in my defence that my keyboard was acting up and it was torture to type anything.
You can send â‚¬â‚¬â‚¬â‚¬ notes perfectly well if you just send them to your payee, as is, in an envelope (preferably with a bit of padding) and hope for the best. I've done it at odd times, and it has worked, but only to family, never to my accountant. If you try to do it through the banking system, you would basically have to change your â‚¬â‚¬â‚¬â‚¬ notes back into Â£Â£Â£Â£ notes at a lousy exchange rate , pay those notes into your bank account, and then get them transferred back into â‚¬â‚¬â‚¬â‚¬s, at a more or less bad exchange rate, and then get them transferred (with or without added fees, depending how hard you try) to your French payee.
But my real issue was with the underlying idea that you want to faff about because the exchange rate is currently "awful". It certainly is, but if you use your â‚¬â‚¬â‚¬ notes now, I guess you will need to replace them sooner rather than later, to spend over here. If and when you do, you have no reason to expect that the exchange rate then will be less awful than it is now: it might just as well be even worse. If I could predict future exchange rates, I would be in the superyacht down in the harbour. Since I can't, I just bite the bullet and change my money when I need to. It works out even over time, and saves you a lot of anxiety.
If you are never going to come back here again, then obviously things might be different.