Comedy in French quite often rely on play of words, regional / foreign accents and idiosyncracies, or pre-conceived ideas tightly linked to the French culture. This is definitely not the easiest way to learn the language.

However, if you are a motivated beginner, you can look for sketches by Raymond Devos, Pierre Desproges or Daniel Prévost, which in my opinion are easiest to understand.

For an intermediate level, you could be interested in sketches by Jamel Debbouze, Gad Elmaleh, Florence Foresti or Anthony Cavanagh. But keep in mind these comedians have or fake accents, and often use slang.

And for very advanced levels, you can try the best of them all : Coluche.

Like Alexis said, it might be hard to learn French with Comedy Skit since most of humorists rely on slang and “inside-jokes” of the culture they are talking to.

I would like to add some to his list, mostly people from Quebec, since that’s where I’m from.

If you want really short sketches, I think François Pérusse is a good choice. You can find most of his work on Grooveshark right here. He made a lot of « 2 minutes du peuple » both in Quebec and France (so sometimes you can even compare the same sketch in Quebec French and France French).

Else, you could go for sketches written by some very well known stand-up comics like Yvon Deschamps, Louis-José Houde or Martin Matte.

If you really want a challenge, and you are up to analyze the texts after listening them, I would consider listening to Marc Favreau and his famous character Sol. His sketches are very well known but could be hard to understand as they play a lot with the meaning of words. His text L’Adversité is very well written (Sorry I couldn’t find a better source).

You might also want to watch this small sketch with Marc Favreau which is an educational and funny episode from a TV show meant to teach [English] students basic French linguistics. The first 8 minutes get you through the whole sketch with translations and then the last 6 minute are the same sketch without any stop (so you can see if you remember).