According to their help page, that’s what they say - they will reclaim it from you.
But you can register yourself and if you’re sending under 10k units/year it’s only €80. I have no idea what Amazon would charge you.
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."
To input your IDs - https://sellercentral-europe.amazon.com/spx/myc/epr-compliance?ref=hp_compport_epr1