Fromage blanc is a French style of fresh cow's milk cream cheese most frequently served as a dessert cheese. Fromage blanc is quite soft, a bit thicker than yogurt. Originally it was made as a fat-free product, but sometimes cream is added to the product, so fat content can vary. It is the texture of thick sour cream.
You can substitute Greek yogurt or see other substitutions below.
If you're out of Fromage blanc or you simply want another option you can substitute one of the following:
Look for this at your local well-stocked grocery store, Whole Foods Market, and sometimes at Trader Joe's and most always packaged in tubs similar to yogurt.
If you're into DYI cheesemaking, this cheese is pretty easy to make. Here is an excellent recipe from New England Cheesemaking. They are a very reliable source for recipes and cheesemaking supplies.