I have collected some French music that is good for learning, and for listening. Here are some of them, and if you know any French songs, add them in the comments!
Joe Dassin - À toi http://www.youtube.com/watch?v=r-QpaFBD6nE
Jacques Brel - Ne Me Quitte Pas http://www.youtube.com/watch?v=i2wmKcBm4Ik
Michel Delpech - Pour un flirt avec toi http://www.youtube.com/watch?v=6tsD85VMeFM
Joe Dassin - Salut http://www.youtube.com/watch?v=vRumiPbbwh8
Joe Dassin - Et Si Tu N'Existais Pas http://www.youtube.com/watch?v=abfQQ1hzN9M
Joe Dassin - Champs Elysées http://www.youtube.com/watch?v=d9V-zUlrhEE
Alizée - J'en ai marre http://www.youtube.com/watch?v=240S04eCCC0
Stromae - Alors on danse http://www.youtube.com/watch?v=7pKrVB5f2W0
Stromae - Papaoutai http://www.youtube.com/watch?v=oiKj0Z_Xnjc
Have fun listening to them :D
I though a while ago about posting French movies and songs. Don't know if it has ever been done, but here is a list off-the-top-of-my-head of French movies and singers:
Older music every single Frenchman knows, or so-called "classics": Joe Dassin, Michel Sardou, Edith Piaf, Charles Aznavour, Jacques Brel, George Brassens, Francis Cabrel, Dalida, Serge Gainsbourg, Claude François, Jean-Jacques Goldman, Johnny Hallyday, Gilbert Montagné
This generation music: Pascal Obispo, Alizée, Patrick Bruel, Patricia Kaas, Bénabar, Matthieu Chedid "M", Mylène Farmer, Florent Pagny, Vanessa Paradis, Renaud, Zazie
Classic movies (but you might have trouble finding a subtitled version and might find it too old or difficult to understand at times): any movie with Louis de Funès, especially "Le gendarme de St Tropez" series, La Grande Vadrouille, La Cité de la Peur (very, very special), La Boum, l'Etudiante, Les Bronzés, Les Bronzés font du ski, La Vérité Si Je Mens, Les Visiteurs, Le Fabuleux Destin d'Amélie Poulain, Astérix et Obélix Mission Cléopâtre... There is so many of them, old or newer
Recent movies that I find depicting quite well today's culture: Les Petits Mouchoirs, Le Coeur des Hommes, LOL (obviously NOT the american version), L'Auberge Espagnole & Les Poupées Russes (not only French), Bienvenue chez les ch'tis, Comme t'y es belle, Le Prénom (a bit more difficult maybe)
Obviously, some will disagree with this list, will say some are missing and others are not classics, especially regarding the movies, so it is not necessary to go into debate other this, I only claim it to be my point of view, and I can tell you many people know these.
If I was to advise you anything, I'd say go with the more recent movies and listen to any song from the singers above. I didn't put any Rap/R'n'b because I don't listen to that, sorry. The recent movies are what I call "Tranche de vie", or "slice of life": it simply depicts the lives of a few characters.
A recent (2013) film, with Catherine Deneuve: "Elle s'en va". Impressionant!
I also would recommended (I actually have never heard of these songs/artists) going onto iTunes and pressing "Free Music" and then going to the Francophone section I have found some of my favourite french artists from there, and also got to see some other music genres. (I am unsure if this works outside of Canada)
I have a few. Music:
(Progressive rock) Nil - Abandon http://www.youtube.com/watch?v=IH2-9YJcfvY
(Progressive rock) Nemo - Apprentis Sorciers http://grooveshark.com/#!/s/Apprentis+Sorciers/4kSrd5?src=5
(Instrumental) Syrinx - Liber Nonacris http://grooveshark.com/s/Liber+Nonacris/2urcs3?src=5
Also the neoclassical band Elend.
For movies I can recommend:
Les diaboliques (1955) http://www.imdb.com/title/tt0046911/
Le Samouraï (1967) http://www.imdb.com/title/tt0062229/
For books I can recommend (no, I haven't read them in the original French - I wish I could!):
The Count of Monte Cristo http://www.goodreads.com/book/show/7126.The_Count_of_Monte_Cristo
The Manuscript Found in Saragossa http://www.goodreads.com/book/show/93180.The_Manuscript_Found_in_Saragossa
J'aime Stromae. J'ecoute:
Alizée - Moi Lolita http://www.youtube.com/watch?v=dDwKPGUIVME
Joyce Jonathan - Ça Ira http://www.youtube.com/watch?v=TxWLybPwBzs
Zaho - Tout est pareil http://www.youtube.com/watch?v=WxeIkAff0C0
Sexion d'Assaut - Ils appellent ça http://www.youtube.com/watch?v=wRFNWBR5y4s