Just a bit of advice to save anyone else making the same mistake as me.
Monese offer a free UK account with no proof of address required. I thought that would mean that I could open one from France. However, the way that they verify is by sending your debit card to the address that you specify, and the app wouldn’t let me enter a French address, it had to be a UK one. So you do actually need a UK address to open a Monese UK account.