You can probably find most American cartoons in French, as shows are dubbed in France. The same goes for TV series, you can find your favorite ones in French ;)
Here's a list of French-speaking shows (some cartoons might be Belgian):
As for French series, I almost only know of crime dramas, such as Falco, Profilage, Engrenages, No Limit, Crossing Lines (not entirely French, it's a European show, but also dubbed in French)...
There are also shows with short sketches: Caméra Café, Un Gars Une Fille, Scènes de ménages, En Famille, Nos Chers Voisins, Kaamelot (might be complicated archaic-like vocabulary), Bref...
As for cartoons, I like Silex and the City (it might be hard vocabulary though), Les Aventures de Tintin (not the movies ;) ), Il était une fois... (might be too childish, there are many series, two of them are more famous: La vie and L'Homme), Lucky Luke, Babar (childish), Code Lyoko, Le Petit Prince.
You can also check out some web-series such as Le Visiteur du Futur (gets more professional with season 3), Les Opérateurs, J'ai jamais su dire non , Noob (video-game related: RPG)...