The book is a retelling of the scandinavian folktale "East of the Sun, West of the Moon" (lassie goes off with white bear, discovers that he's really a prince, and has to rescue him from trolls). The song is referred to as a lovely melody, played on some sort of flute, possibly french in origin, since Pattou (the author) makes it the favorite of the ~18th century french prince. Unfortunately she didn't give any more information on it.