It’s called the SREN bill: SREN = Secure and Regulate Digital Space (Espace Numérique). Specifically Article (Section) 6 of it.
While the situation may be a bit complicated than Mozilla is saying, if the SREN becomes a law, “browser providers” must comply (at least in France) and anyone who does not comply shall be punished. That’s what the bill says in Article 6 (IV).
https://www.senat.fr/leg/pjl22-593.html
Mosilla says they are against such browser-side blocking or similar methods (the bill simply tells browser providers to take any useful action to prevent access—potentially including DNS-level bloking), yet Mozilla also explicitly states that Google-side monitoring would be a better solution—this claim of theirs might be rather worrying, depending on how you see it:
However, even in the worst case, this is going to be France-specific at least for the time being. Everyone else (not in France) should be able to use browsers without a French-Government-defined blocking list.
Perhaps a bit like ~20 years ago, when Americans were not allowed to provide a regular version of Netscape internationally (because back then, that would mean exporting weapons, as strong cryptography was considered a weapon), yet it was okay to download a “strong” Netscape from a non-US country, compiled and provided by non-Americans.