From what I understand, Hitler and Pétain had an agreement whereby the Germans wouldn't interfere in Southern France if the Vichy regime kept "public order". I know that the French collaborators cooperated in the rounding up of Jews in both the Free zone and the Occupied zone in the North, providing the forces and lists of names. So what happened to cause Hitler to invade the South just two years after agreeing not to?
One of the major benefits of the Vichy regime to Nazi Germany was it's ability to keep French colonies and the French military and naval forces out of the war. After the American troops landed in French North Africa at the end of 1942, there were almost no French colonies left where the Vichy regime had effective control. Additionally, the French did not strongy resist the American troops in Algeria, and Vichy figures in North Africa were ambivalent or opposed to resisting the Allies. The Germans felt that this performance would by repeated by any Vichy elements in contact with allied forces, so they assumed control of the remaining Vichy territory in France proper to prevent them from allowing the Allies an easy foothold on the continent.