I am taking a pretty similar class and just wrote a paper comparing Capote's In Cold Blood to the Bennett Miller production of the film Capote. My "deeper meaning" part of the paper was that all relationships are based on a foundation of assumptions you make about other person the relationship. The biggest of these assumptions is that they are a good person and will not kill you in your sleep (or something along those lines). thats the kinda stuff professors are looking for when asking these kinds of questions. find a thesis about the film, find evidence to support it, then find the deeper aspect of it. With my Capote paper my thesis idea was how rumors destroy relationships by breaking trust. After prooving the thesis is when the deep "what can we learn from film" part start to come into play.
thats how i would go about doing it.
sorry for the ramblings