Forgive me if this is eyerollingly obvious information that you already know, but you would look for agents who represent nonfiction, and you'd give them your proposal (in-depth movie reviews focusing on [fill in with some of your favorite themes]), plus a few sample reviews.

The storytelling of your reviews makes this old movies come to life even--as in my own case--when a person has almost no familiarity with old movies.

Maybe you could do it as a Criterion watch-along. Or, you could pick certain actors to follow, or certain directors. Those could be organizing principles. But the appeal for readers would be the drama of your retellings.