UK customers paying in pounds into a UK bank

I just wanted to follow up on a thread from earlier this year and clarify what I think you said in the final post. Here’s the thread:
https://www.startbusinessinfrance.com/forum/answers/opening-a-dedicated-french-bank-account-vs-british

So in the final post, you say that ‘... yes you can cash in your customers into your French bank account’. Does that mean that I can invoice a UK company (in Euros) and that they can pay into a UK bank account (or online account such as Transferwise) in GBP and I can then transfer that money directly into my French AE account with no additional paperwork?

If so, how does that work in terms of currency conversion? Let’s say I invoiced 100€ with an exchange rate for the pound conversion. When they pay the invoice the exchange rate on the day is different and it only converts at 99€; do I need to transfer the exact amount of the invoice into my French account? In that case do I have to take the hit on any deficit (if the exchange rate has gone down) or conversely how would you deal with the surplus (if the exchange rate went up) if it converted to 101€. Or for example, could you retrospectively change the euro value of the invoice to match?

I’m looking forward to your blog on online ‘borderless’ banks as I think this might be the best way providing that an online bank account can be registered as an account for an AE.

Hope you can help

Thanks, Carrie