In the 1930s, Greven was a producer at UFA where he worked with some French directors on multi-language film productions.
In this capacity, Greven produced notable films by French directors including Henri-Georges Clouzot, Christian-Jaque, Henri Decoin, Maurice Tourneur and André Cayatte.
Greven also created the distribution company Société de gestion et d'exploitation du cinéma, which bought and set up new cinemas in France.
Goebbels wrote in his diary that the French had been content with "cheap trash", and he wished Greven would continue to provide them with that.
Goebbels thought Greven's commitment to French cinema threatened the establishment of Germany as the dominant power in European culture, which he wanted to be analogous to how the United States dominated the American continents through its cinema.