You could say that the fox is the prince’s guide, and the prince is the narrator’s guide. (Of course, you could get pretty esoteric and say that the narrator is the guide for us readers, too. That means that, in a way, the fox is leading all of us toward the truth.)
The fox teaches the prince what uniqueness is and how to see the world correctly. He helps the prince understand the value of friendship and taming, and teaches him the patience to acquire those things. The fox gives the prince valuable ideas that the prince cherishes even after the two part ways. Can a guide do any better than to continue guiding, even when he’s out of the picture?