Without wishing to get too deeply into the controversial topic of what is or isn't folk music, I really don't think you can describe O Sole Mio as a folk song. It was written in 1898, the lyrics by Giovanni Capurro and the music by Eduardo di Capua and Alfredo Mazzucchi.
It's one of the best known examples of Neapolitan song, which is a traditional form; but this doesn't make it a folk song. According to Wikipedia, Neapolitan song "became a formal institution in the 1830s due to an annual song–writing competition for the Festival of Piedigrotta." The first song to win the competition was Te Voglio Bene Assaie, which is traditionally attributed to the prominent opera composer Gaetano Donizetti – although this is disputed.
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