Disney's formula has pretty much been lame-ass princess romance stories unless they feel like branching out and ripping off some anime. Lion King was Kimba, the one with what was it, Atlantis? That was ripping off another anime with a hero with glasses who had the hots for some native-type chick in a bikini.
Fushigi no Umi no Nadia, released in the US as Nadia: The Secret of the Blue Water.
To be fair, Gainax borrowed elements from Miyazaki's films for Nadia, though they didn't do anything as blatant as swiping the appearance of the two main characters like Disney did.