Partially, the German occupying forces are speaking English when working together with the French police, especially when no translators are at hand. Is this historically proven?
No, of course not. It's a movie! Just about anyone speaks English in Hollywood movies. No matter what.
Use your common sense. Speaking multiple languages is not common for most people. Foreign languages are taught in high school and above. Not very often on primary schools. The main stream western pupil went to high school and higher after WW1 and more so after WW2. My mum went to primary school only, just before WW2. As she wasn't going to high school, she would do an extra year in primary school. That was at that time the legal requirement in The Netherlands.
The Dutch, for example, are now known to be very good second language English speakers. Before WW2, that was definitely not so. The English proficiency is fairly recent, from the 70's onwards to today. We see the same in Scandinavia, who are also very good in English as a second language.
Now, neither the French nor the Germans are known to be linguistic masters. Why would French dockworkers and German military speak to each other in a third language? It simply makes no sense.
Good communications were quite difficult. The Germans would use German, of course. Which the dockworkers would not understand. One of them perhaps a bit, who would do the translation. A German officer who would speak some French would talk with and by him to tell the others what he wanted them to do.
Which languages were in use during the occupation?
That's what they did. They used the language(s) of the occupied territory together with German. In case of doubt the German original was what legally mattered.
Here a German announcement of the execution of resistance fighters in Maastricht, The Netherlands in German and Dutch.