Two movies come to mind with these details. One of which I don't remember much more about then what you have listed so I'm hoping it's not that one since I wouldn't be able to help in that case but the second movie that comes to mind is
The Lion, the Witch, and the Wardrobe the 1979 made for TV cartoon. The details from this that somewhat match your description is there is a prince (along with his brother, also a prince, and their 2 sisters who are princesses.) But they are trying to catch a white stag. However this scene takes place at the end of the movie. And they have a friend who is a Faun (half goat half human) and I'm pretty sure he plays a flute. I dunno about the tower and shadow though. Hope it helps but with my luck it's probably the movie I can't remember either.