Dvořak, Smetana, Bartok, Kodaly, Bach, Beethoven, Schubert ... so many composers collected and reworked folk tunes that hearing themes in orchestral works lifted from folk tunes is hardly surprising. It is much less often the case that folk tunes were taken from orchestral or composed music, if only because the masses had far less access to it, outside of church or music-hall (where there was a more even-handed, if still fairly skewed, exchange).

It's best to view singable "translations" of foreign folk songs as highly suspect, particularly in songbooks for the primary grades. From the examples I've seen, the "translators" typically take a few characteristic phrases from the first verse and chorus, and make up the remainder out of whole cloth, following some Disney depiction of happy, bucolic life.