Brigitte Fontaine is a one of the most precious treasure of French music, alongside with Brassens and Gainsbourg. There is so much to say on her career: she experimented almost all styles, from chanson, to jazz, pop, arab music and avantgarde, and always with her special touch, between genius and insanity, often radical, always moving. She worked with the best French artists, but also with Sonic Youth and Archie Stepp. To my mind, her style and her importance in music can be compared to the great Nico.
To learn more about her, I let you read the article of wikipedia which is very well done (who says I'm lazy?).
Some of my favorite songs, that just give a little taste of her talent:
Dommage Que Tu Sois Mort (1968)Comme A La Radio (1970)
Lettre A Monsieur le Chef de Gare de la Tour de Carole (1970)
L'auberge (1972)
And to not forget her recent work:
Je T'Aime Encore (2001)