They both like to read books, they both dream of adventure and they are both very graceful but not quiet. Or perhaps Snow White or Cinderella or Aurora as they are all very humbled and balanced.

Like laylastepford said, they are both into reading, seeing as Rapunzel reads three books a day (sure one of them is a cookbook, but still) and they will stand up for what they believe in. They both would like to explore and have adventure, but are still conscious. Belle can be childlike too, like having snowball fights. I can see them getting along. :)

I think Belle- despite what many of her fans firmly think- would really like all three of the classic girls. Cinderella the most, because they're the most alike (assertive, dreamy but grounded, intuitive, indoorsy, etc,), then Aurora for their imagination and grace, then Snow for romantic and spunky sides (though truth be told Belle is less romantic and spunky, but still, I think she'd like Snow and vice versa, they just wouldn't be as close as the others).

^I think the notion that Belle is "indoorsy" seems to come from the sole reason that she likes books while forgetting the film. In the film she says "I want adventure in the great wide somewhere. I want it more than I can tell." Those are not the words of an "indoorsy" person at all but rather an "outdoorsy" person. I also think it is a misconception that Belle is not or less romantic. Her conversation with her father about Gaston and wanting companionship shows she's far more romantic than people think. I think they just get confused because she's picky romantically and refuses Gaston. She also seems very spunky to me as she seems full of energy and courage. When her horse came back without her father she didn't even hesitate to go find him demonstrating her courage and she started the snowball fight with the beast by throwing the first snowball before running around in the snow showing her high energy.