Where are you planning to be in France and for how long? That will be a start in determining wineries to hit up. The Loire is popular [read: heavily touristed] for wine tasting. Personally I'd love to hit the Rhone area in the Languedoc/Provence region, that would be my first stop specifically for wine... but unless you're going to, say, Avignon, it'll be out of the way for you. Do you want to go on an organized, several-day wine tour? Those look pretty freakin' expensive.
Just showing up to some wineries by yourself wherever you happen to be might be a better option... depending, of course, upon the winery. Some may ONLY be open to tour groups and/or private appointments. If nothing else, your hostel would probably have some good ideas.
*edited to add: I did some wine tasting at couple of wine shops in Paris. This might be a more reasonable alternative if you're not going to be spending oodles of time there.