I tried this yesterday, but the "France Connect" website didn't seem to accept my registration (the online process was previously only for those with french passports who were vaccinated outside the EU). I tried it again today with apparent success (I got a confirmation email with a dossier #).

The website didn't work smoothly with my Chrome browser; for some of the fields that must be chosen from a list, I couldn't see all the options. But when I started to type "Etats Unis", that option showed up.

My fingers are crossed for this working and France & Switzerland keeping the borders open.