Douglas Harper's Etymology Dictionary
"characteristic of the common people," 1914, from folk + -y (2). Old English had folcisc "popular, secular, common."
a. (context music informal English) Having the character of folk music
Usage examples of "folky".
I could see that Jenny was sifting these out in favour of more upper-class items, with the folky bare-wood sideboards, velvet dwarf thrones, with its something-I-picked-up here and its got-it-for-thirty-bob there: tastefully timeless.
Granted, they were cheap Cyndi Lauper imitations, but they were also colorful, borderline folky, and rather cute.