Without getting into the perpetual discussion of "what _is_ REALLY a folk song" -- in case anyone is interested, "Blue Moon" is by Richard Rodgers (music) and Lorenz (Larry) Hart (lyrics), from I forget which Broadway musical of ca. the 1930s -- I think maybe "Jumbo," if I remember accurately the drawing on the page of my Rodgers & Hart Songbook. Wonderful song, no matter which category it gets put in.
Could use another Hart-felt verse, though, if anyone happens to be as clever with lyrics as Larry was.
You have 2 chances to sing it this year (3, if you count Valentine's Day): there's a second blue moon in March (I just found this out from Jack Horkheimer's "Star Gazer" program on my local PBS channel).