I have been looking at this today, it’s very confusing! I have registered with LUCID for Germany and that seems to have gone ok. I think you have to use a third party for France - I have been looking at one called ecosistant, but then I read this on Amazon’s Extended Producer Responsibility (EPR) Education link:
If you are selling EPR applicable products on amazon.fr to customers with a shipping address in France, but do not provide Amazon with the valid Registration Number(s) corresponding to those EPR applicable products, Amazon will by default pay corresponding eco-contributions to the qualified Producer Responsibility Organizations(s) on your behalf for sales made from January 2022 and recover these amounts from you. Amazon will pay on your behalf at the end of each quarter or year depending on the EPR category."
So maybe we can just leave it to Amazon to collect, although I’m guessing they will charge us more than we would have to pay if we self-report?