Movie about a vampire who falls in love with a human woman and tries to become human by eating and drinking human food

I don't know about a movie, but it sounds like the plot line (or part of it) from Forever Knight.

Forever Knight on TV.com knight&tag=search_results;title;1

You could be thinking of the pilot of the show that had a different actor (Rick Springfield) in the role of Nick Knight.

Forever Knight: Nick Knight: Cast List on TV.com