Monique, my French-English dictionary gives this definition of "allègre":
Adjective
(a) lively, jaunty, merry (music); light-hearted, cheerful, gay

(It would seem this is the 'Frenchified' version of the Italian "allegro.")

Also, can't "Chant, et m'en apprends ta (tes) danser" mean "Sing(ing), and teaching myself your dance"?   Or can't "Chanter m'en apprends ta danser" mean "Singing in teaching myself your dance">

I get that the gist seems to be she's saying that she's singing in (or "and") learning (teaching herself) to dance in the meadow and to dance cheerfully (gaily).   

Song lyrics sometimes do play fast and loose with normal grammar and twist pronunciation a little to fit the meter and rhyme.