If you were to ask most wine professionals what red wine to pair with fish, they would most likely tell you to stick to white wine. But the opinion around here is that that you should always feel free to enjoy wine your way.
The heavy tannins, bright berry flavors, or deep earthiness of some red wines can be too much for most fish, but there is still a lot of options that might work well, depending on the nature of the fish. Rich, fatty fishes can stand up to a bit of flavor, and can be complemented by a bit of spice or tannins. A fish dish with a tomato sauce can handle a bit of fruitiness. In either case, it may make the most sense to stick to lighter red wines, like Pinot Noir from France or Washington State, or an Italian Chianti.