I think accentless French will pose only minor problems since you can get the meaning of identically spelled words from context and insert the accents accorgingly. In order to be sure I checked with my voice teacher's wife who is a French speaker and she agreed with me.I tried going through some songs to see how much confusion would result and found a sort of a counter example. There is a song called "Le Bal Chez Boule" which should have an acute accent on the e in Boule to be pronounced boolay which is a family name. In the song "En Roulant Ma Boule" the word has no accent and is pronounced bool-uh which means ball. BUT it's pronounced that way to fit the metre of the song. Normally final e's are silent. So in "En Roulant Ma Boule" you have to figure out the pronunciation from musical context anyhow and accents won't help.
I don't claim to be a French speaker despite a grandmother born in Quebec. I learned all my French in school. (Incredible as it may seem I taught it at the Grade 7-9 level some thiry years ago.)
Anyway bring on les chansons en Francais. (und auch deutsche lieder)
Frank Phillips