Pretty sure it isn’t even necessary for Americans. Just show a copy of your card. Even keeping a copy of it on your phone is sufficient or if you have CLEAR you can store it there. When I looked into the health pass I was told it was for French Nationals (if I used the term correctly). Visited the French side twice last trip and was not even asked for a thing. So for future will just keep a copy of my vax card if requested

I just re read. Looks like you may be French so it may apply to you