The "ideal" folk song, it seems to me, would be anonymous, widely known among some sizable ethnic group, expressive of admirable sentiments, beautifully phrased in a fully traditional manner, not too long or too short, sung to a beautiful old melody of unknown date or origin, incorporating bits of folklore or superstition, provably old (centuries preferably), and existing in numerous wonderful variants. What's more, few if any of its singers could have learned it from print or recordings.

I said "ideal." How well something qualifies as a "folk song" depends on the judge's impression of how close it comes to that implausible ideal. (Even "Barbara Allen" seems likely to have started as a stage song.)