alternatehistory.com

After Petain declares that France won't fight on the side with Hitler, the rest of France is occupied - for which Hitler needs many divisions he could use otherwhere. He can't do anything; the few Nazi-sympathizers in the French army already have gone as volunteers to the Russian front.

During said operation, Tunesia has been occupied too, to defend against the approaching Americans. The situation in the North African-Middle East theater becomes more and more difficult for the Axis; Allied ships and planes make it almost impossible to support the troops with what they need (and one has to consider that the Axis have at least the Gulf oil, but not much else).

The Axis troops in Tunisia manage to fight for two months; after that, they have to retreat. The remaining sane people in the German general staff see that this theater is lost, but Hitler doesn't want to retreat and advises them to keep on fighting. In May, Tripolis is conquered; in June, the Allies are in the Cyrenaica; and in July, the fight for the Egyptian delta has begun. At the same time, troops from everywhere from the Empire attack the delta from the South. Now, unrest starts to spread among Egyptian collaborators... they know, if the nazis lose the war, they'll be in trouble, so now there'd be a good time to switch sides...

(I wonder whether the US and GB would try a landing in Italy TTL too, as long as they haven't completely won in Africa / Middle East yet.)