It would depend on context, I think. If we're talking about pets, "Your son has fish" is the appropriate answer. If we're talking about a meal, "Your son is having fish" is appropriate. They aren't interchangeable, though. Also, in the latter one it is not fishes, it's just fish.
This sentence doesn't make sense to me. "The son has fish"? Does this mean they are like his pets? Does it mean he's having fish for dinner? I can't think of a context where this sentence would occur, so when listening I instantly threw away the thought that Fische could be the answer.