I'm editing a video for a friend of mine and he says he wants it to have a gothic look to it, in his own words, "Something like Batman or The Crow." I did as much research on these movies as I could for him and basically told him the gothic look has much more to do with set design than color correction. Still, he has been bugging me to get this done and I don't exactly want to turn my buddy down, so is there anything that could be done to achieve this look and get him off my back?

deep black, faint colors, low contrast, greenish look (Matrix ?)

Yes, "Gothic" is basically a color version of b&w German Expressionism, so production design & lighting are key elements. Color-correction is only a small part (after all, Tim Burton's "Batman" was shot and printed normally, no special post techniques. "Sleepy Hollow", on the other hand, used a silver retention process to the prints to add contrast and reduce color.)

So the color-correction step mainly would be to deepen the blacks and reduce the chroma (color) saturation. But without a Gothic production design and moody lighting, it's not going to feel "Gothic".

Get him to shoot with low-key lighting, preferably in a run-down castle.