I saw a great film, and was immediately inspired. How do I keep my fiction from resembling the film too much?

That is a very very very bad habit to get into. Just because you appreciate something doesn't mean you can go and write something exactly the same as it. If I were you I'd pin down how the movie made you feel and the techniques they used and try and apply them to your own unique idea's. This can be a difficulty in art work and music as well. You can model your technique and style after someone or something else but you should never directly replicate them.