Philippe Petain is ill-regarded in France today, for his role in the pro-nazi Vichy Regime. Prior to that he was a fierce French patriot and nationalist- the Lion of Verdun. So, what if, after the capitulation of the 3rd Republic, he made his way to Algiers with Charles De Gaulle, the up and coming general, and was a joint leader of the resistance? He can have similar political views, hell he can have the same, but he refuses to cooperate with the German jackboots. What does this mean for the Resistance? Would it prompt in fighting? If so, which faction would Britain and America favor? What about Vichy? who else could Germany prop up as a scape-goat, or was Petain the only real option? What could this mean for post war france?
The short/wartime effect would be the dimming of de Gaulle's light in the eyes of the French body politic. He emerged from the war as the unquestioned symbol of the Resistance narrative and the savior of France (with good reason). If the Hero of France was, if nothing else, the figurehead of Free France, it automatically puts a division commander into a far less visible, and vastly less influential, position. What impact that has on postwar French politics is difficult to gauge, the political situation was... fraught, although If Pertain was the Face of Free France during the war he would likely be the "king maker" post war.
It is unlikely that the Germans abandon their "Vichy France" concept. It afforded them all the positives of Occupation with almost none of the manpower costs. They would find someone else to collaborate (there is
ALWAYS someone who will collaborate) and proceed as happened IOTL. Someone else sits in the dock post war and is convicted of Treason, since they are certainly not of the same status as the Lion of Verdun, they likely dance Danny Deever.
The WAllies are absolutely delighted to not have to deal with de Gualle as much directly. Churchill seriously disliked him, Stalin thought he of little consequence and FDR
loathed the guy to an amazingly intense degree.