If you mean actual names of wines, there are hundreds.
If you mean the main categories of wines, there may be more than 5. Here's a few:
- Beaujolais (red wine from South Burgundy)
- Bordeaux (whites, reds, and many very sweet dessert wines)
- Bourgogne (more robust red Burgundy wines, a few whites too)
- Champagne
- Côtes du Rhône (mostly lighter red wines)
- Rosé de Provence (light and sweet "pink" wine)
- Vins d'Alsace (gewurtzstraminer, pinot, riesling, sylvaner, ...)
- Vins de Loire (mostly whites: muscadet, pouilly fumé, sancerre, vouvray...)
- Vins de Savoie (Savoy wines such as Apremont)
- Vins du Jura (vin jaune, yellow wine, vin de paille, straw wine)
There are more detailed sub-categories in each of these. For instance Beaujolais wines are divided between Chiroubles, Juliénas, Moulin à Vent, Saint-Amour, etc.