What if Hitler hadn't invaded Vichy France in response to Operation Torch, in November 1942?

Operation Torch was General Eisenhower's invasion of French North Africa, in an effort to open up the Mediterranean to the Allies, and totally eliminate the presence of the Axis powers in Africa. Because the U.S. had maintained relations with the government of Vichy France, it had been expected that the French would not fight or contest this American invasion. The Americans were disappointed. The French fought hard and well. General Patton commented that if there had been any Germans backing the French up, the Americans would never have even gotten onto the beaches at all. After a week of heavy fighting, the French agreed to a ceasefire, but only because the Nazis had just invaded Vichy France in direct response to Operation Torch, and they felt they'd been stabbed in the back. Even so, the French only agreed to maintain the ceasefire on condition that Admiral Francois Darlan -- an out and out Nazi -- could remain as governor of French Africa. Darlan continued his policies of exterminating democrats, free french and jews in French Africa, with General Eisenhower's full approval, because Eisenhower didn't have the manpower to conquer French Africa if they continued to resist. Perhaps not entirely surprisingly, Darlan was assassinated just a month later by a free french agent, probably with support from British and American intelligence. So, what if Hitler hadn't chosen to stab the French imperialists in Africa in the back, by invading their base in Vichy France? Did he really have to do this? I suspect that Hitler didn't realize how much in sympathy many people in France were with him, at the time. Hitler's dream had been for the French to join him in declaring war against Britain. Actually, Operation Torch might have gotten them to do just that. After all, what did they have to lose, they were already being attacked, and invaded. It's perfectly possible General Petain might have been persuaded by operation Torch to declare war on Britain and the U.S., thus offering the possibility of millions of new soldiers, hundreds of new military divisions, to Hitler's war machine. Furthermore, if France had ceased to be neutral, but become an active belligerent on the side of the Axis, it might have been impossible for Francisco Franco to maintain his Axis leaning neutrality. With both Spain and France on the side of Germany, the entire calculus of the war becomes dramatically altered. With hundreds of new divisions available, Hitler almost certainly retains control of Stalingrad, or is able to retake it, in Russia, and makes further conquests. Any invasion of Western Europe becomes impossible, Hitler has perhaps another 100 million people to draw on for military manpower. I'm not sure if Hitler actually wins the war, but, he might not lose it. Some sort of negotiated peace seems likely, under these circumstances.