This is a French film based on a play by Arthur Schnitzler. As I recall I read the play in high school, outside of normal classes, though how many in high school or how many classes are normal is debatable. The play, and the film, traced the migrations of love through the social classes. If I recall correctly, in the play, but not in the film, there was also a bit of implication that it was tracing the course of venereal disease, syphilis, through the various social strata. The play thus embodied the idea that became popular in the 1980s that in sleeping with a person you also slept with their entire sexual history.
The film starts with an encounter between a prostitute and a soldier. As you might expect in a film titled La Ronde, what goes aronde comes aronde, and the film ends with the prostitute and another client, a count, shown in the picture above.
Anton Walbrook as a role as the author of the piece. He does not stand outside the action but interacts, to a limited extent, with the characters. His presence, and his interaction and manipulation of the characters suggest a mechanistic view of the drama. This is reinforced by imagery of a merry-go-round, and of the film set itself.
The play, and the film, served as the inspiration for several other films, including one in the 1960s with Jane Fonda. This was in the days before Jane decided, mistakenly, that she had a brain.