Part of me really wants to know the answer, but the majority of me doesn’t, because like it's been previously stated, that's part of the Fool's mystery.
However, whenever I mention or think of the Fool I call him, well, a him.
I also agree with The Faery Queen, in that I myself prefer the idea of Fitz and the Fool in a gay relationship rather than the Fool being a woman and them having a man/woman relationship. Not that it ever seems to move in that direction, but if it did, that’s what I picture, for whatever reason, I can’t exactly explain it.
I don’t know what he is, I think he’s not human and therefore his “plumbing” is not as simple as ours is perhaps, but I also think it isn’t as important. If I had to pick though, I’d pick male.