The two things that everyone mentioned about The Triplets of Belleville back when it came out were that the movie was animated and that it was deeply, bizarrely, weird, surreal, and nonsensical.
Somehow from these remarks I concluded (incorrectly) that it was animated with puppets, using some kind of weird stop-motion technique (instead, it's a neat mix of cel animation and CGI), and that there was no plot to speak of (instead, there's plenty of plot, and it's not especially hard to follow).
At any rate, now that I've seen it, I would say that most of the reviewers I heard from at the time were kind of off-base.
I'm not going to talk much about the movie itself here; I'm mostly going to just disagree with most of the critics I've seen review it.
I would call the movie "charmingly odd." I would also mention, as almost none of the reviewers I saw did, that it has essentially no dialogue; I was concerned by the fact that there are a couple of voiceovers in French early on, sans subtitles, but those lines don't supply any necessary information, and for most of the rest of the movie there are no spoken words. (One of the DVD commentary sections shows, in passing, English subtitles for a couple of the French bits; understanding the actual words turns out to be just as unnecessary as it seemed.)
But I would not call the movie, as Roger Ebert did, "creepy, eccentric, eerie, flaky, freaky, funky, grotesque, inscrutable, kinky, kooky, magical, oddball, spooky, uncanny, uncouth and unearthly." Ebert added, "I can't think of another film 'like' it." Relatedly, Frank Swietek wrote "it's not supposed to make much sense" and "It's barely accurate to speak of a plot to the picture," and Kenneth Turan of the Los Angeles Times wrote: "A truly out-there piece of comic animation, [...the movie] takes us into a world that can barely be described, a world unlike any we've seen before."
That all makes it sound like it's not only sui generis but so deeply weird as to be beyond anything seen by mortal eye before. I disagree. The movie seems to me to be quite a bit like a feature-length version of all those animated short films that used to show up in annual animation festivals and the Tournee of Animation. (Plus some explicit references to 1920s and 1930s Max Fleischer animation.) It has the same kind of offbeat sensibility, the same affection for running gags, the same willingness to go off on a little tangent for a few seconds to show us a fun subplot or mini-story or joke that's irrelevant to the main story, the same kinds of sight gags in the background.
I like Ebert's phrase "the Marquis de Sade meets Lance Armstrong," but more as a joke than as a description of the movie. Ebert added: "Most animated features have an almost grotesque desire to be loved. This one doesn't seem to care." I disagree with that too; I think this movie tries hard to be charmingly odd (and oddly charming), and more or less succeeds.
So, anyway, I found the movie mostly fun, often charming, a little unpleasant in places, kind of fluffy, and certainly odd; but not nearly the extravaganza of the uniquely and incomprehensibly surreal that most of the critics seem to have seen. I'd have watched it sooner if I hadn't had such a distorted idea of what it would be like.
P.S.: The making-of material makes clear that Belleville is meant to be a mix of Paris, New York, and Montreal, and I was assuming that the water that was crossed was meant to be the Atlantic (he said, trying to avoid giving too much detail). But Wikipedia suggests that Belleville in the film is meant to be a variant of the real-life Belleville region of Paris. I can see a way in which both of those things could be true, but I'm not sure whether the latter actually is true (that is, whether Belleville in the movie was meant to have anything to do with the real place with that name). Anyone know offhand?