Article 6 (para II and III) of the SREN Bill would force providers to create the means to mandatorily block websites on a government provided list encoded into the browser.
Best solution is that France doesn't get any browsers through direct downloads. They will force to download them from other countries and tell in EULAs this is not to be used in France.
I don't know what the French government is smoking if they think this is even remotely enforceable. While Google and Mozilla might comply, there's a lot of browsers that won't. And some of them will be Firefox variants. We'd likely see a 'Feu Renard Sans Bloquant" (I don't actually speak French).