The kind of scenario described by Karl is imaginative (I don’t think I’ve ever previously heard a scenario along those exact lines), but I think it’s improbable for a number of reasons. Hitler had a visceral hatred for France (dating back to his WWI experiences, and to Germany’s 1918 surrender, which Hitler regarded as a national tragedy), and his 1940 conquest of France was to a large degree (though not exclusively) motivated by a desire for revenge; it wasn’t entirely about securing his western flank for a campaign against the Soviets. The concept of Hitler defeating France and then basically saying to the international community “There, I’ve proved my point. Now, shall we all sit down and discuss a reasonable settlement?” strikes me as being out of character with Hitler, who wasn’t known for his reasonableness or for his subtlety. And I’m not sure he would have found any buyers among the international community, which by then understood that treaties with Hitler were meaningless stopgaps at best and a prelude to invasion at worst.
The concept of Hitler unilaterally withdrawing from France and leaving behind a puppet regime in charge of the whole country would probably have been problematic both to Germany and to France. Germany did set up a few puppet regimes during WWII, but as far as I know they were all small, obscure, and buried deep inside German-controlled Europe. In other words, they were strategically inconsequential. The concept wouldn’t have worked in France, which is a large country, which controlled a vast colonial empire, and which has an Atlantic coastline within eyeball distance of Britain on a clear day. Hitler was very worried about that coastline, as can be seen from which parts of France he chose to keep under direct German occupation; it constituted a threat to his western flank which could not be eliminated even with France under German occupation, and it would have been even more of a vulnerable area if it had been left in the hands of the Vichy regime, which Hitler rightfully distrusted. The Vichy regime was a collaborationist regime, but it was too much of a loose cannon to be considered a puppet regime; part of its agenda was maintaining the fiction (in its own mind as well as among the French population) that it was its own boss. Consider what happened when the Allies invaded North Africa: Germany was angered that the French colonial forces had not resisted more energetically, and it promptly occupied the southern part of France controlled by Vichy; the Vichy regime responded by scuttling its fleet to keep it out of German hands. True puppet regimes are much more docile than that.