In practice, most of the lower level officers and Vichy government officials were anti German, against collaboration and against German occupation.
Resistance to a German invasion, will be light at first due to confusion, orders from above etc but would coalesce quickly. The amount of troops the Germans could move across quickly was pretty small in OTL. I could see an occupation of Tunis, Bone and Algiers but the interior would be restive and its a long way to Morocco.
Then the Germans have to feed the place, which was largely supplied by the USA. The place doesn't seem worth it. The Allies could re-invade whenever they are ready.
This only seems plausible in a no Barbarossa or a victorious Barbarossa scenario where you could commit a large contingent of air force, including lots of JU52s, then you could interdict Atlantic convoy routes and bring forward submarine bases. Perhaps the Germans would want to declare the independence of the colonies from the French to gain some internal support.
Really the Germans got a lot from having Vichy around, especially when doing Barbarossa, a secure area for a couple of campaign seasons, a blockade hole, their agents could flaunt themselves all over the place, a place they didn't have to supply.