At its heart—its glowing, beating heart —Amélie is a romance. Not only is it set in the city of love, but it's also about finding love. We're not necessarily talking about love with another person, although that is a big part of the movie; we're talking about finding the romance in everyday life itself. Think of the beginning of the movie, when the camera lingers on two wine glasses dancing on a tablecloth: it's romance in normal, everyday objects.
The film is also a comedy—but it's not necessarily a romantic comedy. The two main characters don't start off hating each other and then growing to love one another after a series of random mishaps. In fact, they barely have any scenes with each other until the very end. The comedy comes from the supporting characters, like hypochondriac Georgette or cranky Collignon. More specifically, it comes from the cruel—but deserved—pranks Amélie plays on him.
Finally, the film shows us a magical vision of Paris. If you're not from Paris, that makes it a foreign film, but even if you are, the film is so colorful and whimsical that it might show you a side you didn't know existed.
Amélie's imagination sometimes takes over, with her portraits of animals talking to one another or her wild, made-up stories of other people's lives. So even if elves and wizards and magicians don't play a big part in Amélie's life (unless she decides to dream them up), the film is also a fantasy in the sense that Amélie's always daydreaming, making things a little more fantastic than they might otherwise seem to be.