OTL, after the fall of Paris Philippe Petain (as he confessed in his Autobiography - The Lion of Africa) briefly considered joining the Vichy collaborators in the hope that it would minimize suffering on part of the French populace. But as we all know, Marshal Petain decided that he would rather "die a free Frenchman than live as a German slave" and evacuated to North Africa. From Algiers, he would command the Free French forces and serve as "President of the Fourth French Republic". Eventually the Free French would land in the South (in sync with Normandy) and liberate Paris.
But what if the Lion of Africa - the man many consider to be the greatest French hero since Napoleon - had chosen to collaborate? Would French Africa gone to Vichy? Would Petain be executed post-war? How would the war in North Africa and the Mediterranean develop? And who would've led the Free French?