Hello @Carl Schwamberger, this was something I wasn't aware of.Perhaps I missed it, but a consideration with a more pro Axis France than OTL, is relevation of the Enigma machines vulnerability. In 1940 France had progressed as far as Britain in reading the Enigma decrypts, they also had all the escaped Polish cryptographers. OTL Petains government concealed what they knew of the Enigma machine, and kept the Poles along with their French cryptographers at work reading what they could of German radio traffic. In early 1943 the Poles fled, some reaching Spain & then the UK, a few others hid in France.
If Petain orders the Deuxime Beureau to share its knowledge of breaking the Enigma system, then it is possible the Brits are shut out of German radio signals for the rest of the war. That has some knock on effects.
Edit: Petain may not be the decision maker in this. Even if there is no policy of sharing important intel with the Germans a profacist French intelligence officer may leak the facts to the Abwehr.
This is a big butterfly that I didn't considered, though the impact may be lesser than expected due to the sheer superiority of the Italo-British alliance in terms of both air and naval power in the Mediterranean theatre (the main one for this TL).
Since no one had voted besides @pls don't ban me the next chapter will be on the Balkans (expect meaningful deviations from TL...)