Steve is a documentary-maker, kind of like Jacques Costeau, although he's well on the way to being a has-been pothead. And unfortunately, his diving buddy gets eaten by a "jaguar shark". And his long-lost son shows up. And his wife is on the edge of dumping him. So he's under a bit of strain.
Not laugh-out-loud funny, but well-acted and imaginative. Most of the humor is understated and embedded in context, instead of gags. Zissou's ship (the Belafonte) devotes major resources to the sauna and kitchen; the lab space, not so much. Nearly all the sea creatures encountered are (literally) fantasic, CGI-generated. It's not clear Zissou knows anything at all about them; he makes up names for them on the fly.
Willem Dafoe could make a comedy very easily.
And I didn't know Bud Cort was in this until the credits. And then I said, "Holy crap, that was Bud Cort?" And then I looked at his IMDB entry; he's been making movies steadily for years, but I've managed to avoid seeing any of them since MASH in 1970. Well, I guess I don't look much like I did in 1970 either.