Evil control freak that he was, wouldn’t he have wanted to rule all of France without fooling around with a puppet regime that only covered *part * of French territory anyway?
Germany didn’t have the man-power to occupy the whole of France. Not possible. So they occupied the part closest to Britain, and let Vichy control the rest, under their orders. Strictly a logistics problem.
It got France out of the war, got Alsace and Lorraine back for Germany, and let the Germans base all along the Atlantic coast so that they could intercept British shipping and launch the Battle of Britain/Sealion (hypothetically). What advantage would there have been to occupying the country?
And it wasn’t long before Germany did occupy the rest of France – November of 1942.
First, there was no much point in occupying the whole country. The most industrialized areas, that were situated in eastern and northern France, were under German control (the “border” wasn’t following exactly the cease-fire line, but was modified to include industrialized areas in the occupied zone, and exclude areas that weren’t economically interesting), along with all the atlantic coast and its ports.
Second, had the armistice not be signed (and I assume that “I’ll take the whole country” wouldn’t have been an acceptable deal), France would still have been at war with Germany which means that her fleet and colonies (in particular in north-africa) would have stayed on the allied side instead of being neutral/friendly.
I would note that as soon as there has been a point in occupying France, after operation Torch, because
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the Mediteranean sea became a vitally important area
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An invasion of southern France by allied forces became possible in the future
3)The rallying of Vichy France civilian and military authorities to the allies negociated by one of the highest ranking Vichy France official who happened to be present showed that the Vichy France authorities couldn’t be relied upon by the Germans
- There was a risk that what was left of the french fleet could try to join the free french forces in north africa (actually it was scutled when the German army invaded the “free” zone)
the German forces didn’t hesitate for a instant to occupy Vichy France, showing that it wasn’t occupied before in all likehood only because there was no point in doing so (and of course it required manpower which was more useful elsewhere).