[Tax-chick]

Aside from church music, it’s very difficult to find musical pieces this old. My college choir did one in Polish, and there are a few troubador songs for which melodies are guessed at.

[AnAmericanMother]

That's 'cause the monks were the only ones with sense enough to write their stuff down. The troubadours built on the sand, in a sense. At least they wrote down the words.

We do have popular songs that found their way into church music as the underlying basis for early polyphonic masses . . . the most famous one comes from a later period, early 15th or possibly late 14th century:

L'homme armé "The armed man, the armed man should be feared. Everywhere it has been proclaimed, that each man should arm himself with a coat of iron mail."

Guillaume DuFay, one of the great composers of the 15th century, wrote a Mass based on this melody (so did about half the composers of the time, it seems - there are over 40 settings based on the tune). See if you can pick it out of the Kyrie:

DuFay: Missa l'Homme Armé: Kyrie

Johannes Ockhegem: Missa l'Homme Armé: Kyrie

The third of the great trinity of composers of the fifteenth century was Josquin des Prez - usually just known as "Josquin".

Josquin: Missa l'Homme Armé: Kyrie

Josquin also wrote one of the sweetest and saddest laments ever sung, for his master Ockhegem.

La Déploracion de Johannes Ockheghem

Translation provided in the comments below by yrs truly.

[AnAmericanMother]

A more period-correct performance of the "Déploration" - with a different and more poetic (but somewhat less accurate) translation . . .

Nymphes des bois

A perfectly period-correct performance would have a very nasal tone . . . think country Sacred Harp singing in the Appalachians . . . but as our music director says, nobody could stand it. I'll settle for no vibrato!