Puppet regime set up in Paris, (nominally) run by the Orléanists. When Germany invades Algeria, Parliament forces out Reynaud, and then surrenders.
More interesting would be if Pétain had joined the Allies when the Germans invaded Vichy, following Weygand's advice.
A puppet regime in Paris, you're right, but not with Orleanists (WTF ?!?), just with some "collaborationnistes" (Déat, Doriot, Bergery, etc).
In Algiers, indeed, there would have been divisions and fights among French between those who would have tried to negotiate with Germany anyway.
But Germany would have been forced to occupy all the South of France and to waste troops, that wouldn't have been used in the Balkans and in Russia.
So, I'm not sure Germany would have invaded Algeria, unless Mussolini again tried something and screwed up the whole thing...
Either, after some time, some French around Reynaud, de Gaulle would have anyway gone to London or to some colonies readier to fight against Germany, or it would have been a mess until a big (and sooner) intervention by British and American troops. And maybe the Anglo-American would have taken more French ships...
And with troops wasted in southern France, Germany would have lost quicker in the East.
Remember that the so-called "zone libre" wasn't at all a victory grasped by Pétain, Laval, Huntziger, but a convenient way for Germany to let the new Vichy regime maintain the order in the non-strategic part of France....
So, no great difference for France (except a big moral difference: less dishonour with a government that collaborated with Nazis), but a shorter war in Europe. A big difference for the world...
