French roast is a dark coffee roast -- meaning that the beans have been roasted at a higher temperature than many other roasts. It is darker than City Roast and Vienna Roast but not quite as dark as Italian Roast. It is the darkest roast that most Americans are likely to drink, and most will prefer lighter roasts (City Roast is the most common in America, although it usually isn't called that on the package). French roast is commonly used in espresso blends.
The darkness of the roast is dependent on roasting temperature; French roast reaches temperatures of about 240°C (464°F), meaning that it is just past the second crack, and firmly in the dark roast category.
French roast coffee is generally described as robust, rich, tart, and as having 'low-acidity' (which is descriptive of flavor, not pH balance). This is somewhat variable; some French roasts are described as smoky or light-bodied. Personally, I just describe it as strong, not being much of a connoisseur. The beans are oily and very dark brown, although this is less apparent once they are ground.
You may also come across 'French roast blends', which is just weird marketing talk -- a way to get the word 'French' onto the coffee can. These blends probably contain some French roast, but more than that cannot be determined without inspecting the label.