The series has been dubbed La première folie des Monty Pythons (The Monty Pythons’ First Folly), but the original title is almost always used as far as I can tell. As far as I know, there is no official translation of the phrase itself ; I have actually seen it used as is in French (granted, from English literate persons).
I don’t know of any official translation. I’ll propose et maintenant, sans transition (literally: “and now with no transition” [to ease the change of topic]). It, like “and now for something completely different”, was a catchphrase of a TV presenter (maybe not from the same generation) used as a transition phrase between two topics in a TV program. I think that presenter was Patrick Poivre d’Arvor, who presented the TV news program with the largest audience in France for two decades, though I don’t know whether it originated with him. The phrase gets a lot of use, I think most French people today will recognize it as something they’ve heard before (even I do, and I’ve probably never watched that news program).
I don’t think the series was widely known in France so the reference will not be recognized by many people. In fact I would say the english version might be as much recognized as the translation used in the dubbed version which is “Et maintenant, quelque chose de différent.“
I’ve just found the answer in “The Pythons Autobiography by The Pythons”. French version is:
Et maintenant quelque chose tout à fait différent
I guess it’s the best translation we can get.