One of the more influential laws would be the S.T.O, Service Travail Obligatoire, translation: Compulsory Work Service. It sent thousands of middle aged men and women to work in factories for the German war effort. This law was first passed by the Vichy government in September of 1942 and would be slightly modified later on.

Also, Phillippe Petain's cooperation with the Nazis led to your "average" anti-Semitic laws under the Third Reich (Curfew, confiscation of valuable assets, exclusion from most public settings and eventually deportations...)

As for the "Commander of the German Paris Garrison", this position was more of a ceremonial position and called the Military Governor of Paris. The rank was at least that of Lieutenant-General.