I’m trying to practice my French; I’d like to watch a TV series in order to improve my listening. A series specifically (as opposed to, say, a movie) because A, I can watch it in digestible chunks and B, it (presumably) has continuing elements that build on each other. I would like for it to be streaming, not some sort of weird illegal torrent thing, mostly because I’m too technologically inept to understand those. 
I don’t really care about the topic or quality of the show as long as it has a narrative thrust and I can watch it from the beginning, but bonus points if it’s good. I’d prefer no subtitles, and as high-res as possible. Obviously this is excessively picky, so if you know of anything that fulfills only some of my factors, please post it anyway! Thanks a bunch for your help. I’ve found a number of sites that tune straight in to extemporaneous French TV channels, but that’s not what I’m looking for.
I can’t speak with regard to French, but I have found a wealth of broadcast material in German on the Internet, courtesy of the broadcasters’ websites. For example, ZDF appears to include the German version of The History Channel, and they let you watch complete episodes. They’ve done a three part history of the Nazi takeover in 1933 (I guess it’s The Hitler Channel there as well), and a ten part series on German history from about 950 to 1900–and you can watch as many episodes as you have time for. There is lighter content available as well, such as soaps, detective shows, travelogues, and comedy. Of course there’s also news. In many cases, you can livestream the current broadcast, although otherwise you may only get a message saying that such content can only be watched via actual television, due to copyright provisions.
As for streaming there’s usually nothing to it–just click and watch. But you do need broadband Internet connectivity, and, I would say at least 1.73 MHz duo-core processing and 1G RAM. That’s cutting it a little close, but it can be done, and any computer made within the last couple of years should have at least that.
ETA: If you don’t know the French stations, you can always look in Wikipedia, which has lists of broadcasters in various regions and countries.
This is the french site of the CBC, the Canadian Broadcasting Corporation.
I usually do not watch french canadian TV, so, I can’'t really recommend anything, but if your french is decent, you might be able to navigate the site and find something to your liking, assuming any of their french shows are streamed.
If you don’t mind 3-5 minute-long, self-contained webisodes, may I suggest http://www.tac.tv/ ?
Other Canadian French-language channels are TQSand TVA. Some of the shows they carry are the French versions of American shows, if you want to watch something you may have already seen and compare it (I cannot vouch for the quality of the translations…humour and nuance are so easily lost in translation, and I prefer to watch things in their original languages).
I really don’t have any particular recommendations, largely because I don’t tend to watch entertainment TV in French. Most of my French TV watching will be news and sports!
What mnemosyne and J-P L said. I’ll add TFO, the former French arm of TVOntario, which is now an independent organization; and TV5, the Canadian part of an international French-language station.
Hopefully, someone else can add programming from France.
About 10 years ago we got TV5 on DishNetwork to help our daughter with her French. Not very expensive, assuming your dish is pointing at the right satellite. It carried both French Canadian French and French French programs.
I’ll just point out that all the Canadian channels mentioned above are likely to have dramas in Canadian French. Dubs are likely to be in a more neutral accent, but local productions will be in Québec vernacular.
This site has French television programming on-line, but it appears you need to be in France to access it.
Your best bet, in my opinion, is going to be TV5 like Voyager mentions.
Of course, you might also decide to go for Québec French after all and waste your days watching Les têtes à claques.
Reported.
Netflix has some content in French.
(And if you select French as your preferred language everything will be French, I don’t know about the quality of the voice-acting)