I would guess it is a fowler. That actually was a lot more common a weapon then people give it credit for. Because the smoothbore fowler was able to shoot birds and small game, while at the same time load a roundball and take VERY large game animals. It is still a beautiful weapon.
Since we are talking about old weapons I might share one of mine....
I was lucky to inherit a .22 caliber rifle from my Great Grandfather. I actually shot it once and it was exciting, but also kind of worried me, because of the rifle's age. But I then cleaned the rifle and put it up on a plaque. It was the first .22 caliber rifle that Sear & Roebuck sold (according to my Dad). My father claims that his Grandfather paid $4.00 for it. It was for shooting hogs and cattle on the farm (for butchering). When I show it to people most of them can not figure out how it even works.. its pretty cool actually.
The rifle is a "Provin Favorite" and an amusing thing happened when I was at a art gallery once. On the wall in a glass and wood case was a rifle hanging there, and it was an identical rifle to mine. As I was admiring it, the woman who ran the gallery kind of puffed up and asked me if I could figure out how it worked.. I just smiled and explained not only how to shoot it, but who made it and who sold it. She was shocked and asked me how I knew. That's when I told her I had one identical to hers. She then began to question me more about the rifle and finally asked if I would be interested in selling mine. I told her it was my Great Grandfather's and was not for sale.
Just thought you people might be interested.