The mute e at the end of French words is normally silent in speech, but it used to be pronounced, and so in old songs it often has to be restored for the sake of the syllable. For that reason, it is also often pronounced (facultatively, as the grammarians say) in recent songs where an extra syllable is wanted. So it's "Cha-grin d'a-mour du-re tou-te la vi-e". For an example of the facultative use, listen to Marlene Dietrich sing "La Vie en Rose": "Et ca m' fait quel-que cho-se".   The schoolbooks say to pronounce the e in "me" but not at the ends in "quelque chose", but with poetic license it is the other way around.