Both titles "Vieilles chansons et rondes" and "Chansons de France" have been republished by "L'école des Loisirs", I bought them both for € 5.50 each last year. You can order them at Amazon.
You'll find "Vieilles chansons et rondes" to read on line on The International Children Digital Library.

Genie, your translation is good. Just in "Un froc de bure", "bure" is the thick brown woollen fabric the monks' robes are made of, whether it's homespun or not. My Collins-Robert Fr/Eng dictionary gives "psalter" as the translation for "psautier" = book of psalms