There are about 400 different types of French cheeses. There all over 900 known cheeses in the world. The exact number varies depending on how one counts them (e.g. all types of cheese, or only those that meet the AOC standard).
However, one also needs to consider that much of the cheese in France is made by small independents or co-operatives. For a single type of cheese, there may be several hundred different producers. The cheese from these different producers will be somewhat different due to variations in the milk, yeast, and production approach used. Some producers will take milk from only a single farm, while others will use milk from several selected farms. Individual cheese makers may have different quality standards (for example, some will insist that the milk is 100% bio). Some will produce cheese in a highly controlled and technically advanced environment, while others will use more traditional means. All these differences can result in a given type of cheese having many different versions in terms of texture, taste, quality and price.
Furthermore, cheeses can be aged for different periods of time, changing the taste, texture and aroma. Each producer may provide mild (young), medium and strong (well-aged) versions of their cheese. This is of course relative, a young Roquefort will have a stronger taste and smell than an old Compté.
Consequently, if one considers the differences resulting from individual producers and aging, it is more accurate to say that there are many thousands of types of cheese in France.
~I HOPE I HELPED~
I guess theres about 670 well known cheeses, but many more out there that are unnamed.