I've really hesitated to revive that thread by posting in it (having read the rules and all), but the shere astonishment I felt by reading it compelled me to add something.
Astonishment? Why? Because no one mentioned George Brassens. Yet, for the very purpose for which this thread has been initiated (and besides the general awesomeness of his songs), he really is a must-listen: the vocabulary is mostly simple, but rich, the grammar is excellent, and the lyrics are distinctively articulated, and usually not too fast. It would really be the first I would recommand to anyone wanting to get used to listen to French, and catch some vocabulary by the way.
Charles Aznavour would be a good one, too. And if you want an initiation to puns in French, Bobi Lapointe.
For something more "pop-rock", Jacques Higelin is a good choice, too. Or, more "indy", Autour de Lucie (I read somewhere that this band is not quite unknown in the USA). I'd recommand Noir Désir, as well, for its rich lyrics, yet since it's a rock band with a "big sound", the words may not be always as easy to catch.