German translation would be very close: Schöne Jungfrau, though Reinhold tells us of a German version called "Graf und Nonne"

I don't know the answers to Steve Gardham's questions, though I thing the motif is fairly widespread. I only learned of the song when because the air was presented in an instrumental workshop at "Scandimoot" festival.

the story is just a bit like Martin Guerre and Sommersby and the Scottish song Is Gur Milis Mórag https://www.omniglot.com/songs/gaelic/gurmilismorag.php and even a bit like "Johnny Todd". But I can't think of anything closer to the story of Skjøn Jomfru.

Is it the theme of the song or the title which rings a bell? There's a very different Danish song called Jomfru i Hindeham , in which a man kills a young deer whose corpse is not a deer but his own sister.