That's roughly patterned after a Henry English pattern rifle, probably somewhat less roughly than a TC Hawken was patterned after a Sam Hawken rifle. To my knowledge there is no record that the Henry's ever made one of these left handed or as a smoothbore. I have handled an original one that was bored out smooth after being pretty well shot out. They also had an english-type patchbox and 42-44" barrels with a slight swamp.
BTW, the Henry's did contract for a few smoothbore Northwest guns with AFC during the 1820's but were outcompeted in this market by the English makers. However, according to the remaining records, the Henry's were the top rifle contrators for the American Fur Company until sometime in the 1840s. Like Gray Wolf mentions their number one product was their Lancaster pattern follwed by the English pattern. In 1834, they began producing a rifle referred to as the scroll guard or new English that would eventually outstrip and replace the old English pattern. All of these were brass mounted, but there are a few records of iron-mounted guns being ordered by the upper Missouri outfit around 1830. What these guns looked like is only speculation. Later on the Henry operations started making half-stocked plains rifles and eventually patented a design for a single barrel break-open shotgun with an external side-mounted hammer. They operated over about 4 generations if I remember correctly from before the Rev war to the 1890's.
You can find some info on Henry trade rifles in Hanson's Hawken book available from the Museum of the Fur Trade and the KRA and Kaufman books There are other references I can provide, but most are out of print. PM me if you want citations.
Sean