This subject has been discussed elsewhere in the past and the fact is the gun was an original double side by side with a smoothbore and a rifled barrel. They were known in Africa as cape guns and are like this one on TOTW
http://www.trackofthewolf.com/Cate...catId=12&subId=78&styleId=266&partNum=AAI-465
While the type may have been a bit unusual they were not unknonw in the west of that era.
Side by side double guns of varying quality were widely available and popular during the 1830's and later - remember JJ is dated post 1846-48. Double guns, including finely made English ones, show up in western trade records especially the HBC records and in St Louis they were sold by most dealers (see the 1830's St Louis adverts in Charles Hanson's book on Hawken rifles to see the variety of guns and other weapons available - and if you were a western trapper and had the money you could order what you wished and have it delivered.)
How the Indian got it? as others have noted several ways were possible: a gift, stolen, etc.
While the most common gun of that era and in that place would have been an American made long rifle of some style/type many other types were available as well - Bridger reportedly carried a swivel breech at one time and McKenzie, factor at Ft Union in the 1830's, ordered a Billinghurst revolving long gun to go along with his chain mail shirt.
Also by the 1840's hunting expeditions in the west by the rich were becoming more and more popular. Capt Stewart, who carried doubles by Manton and also supplied at least one of his retainers with such a gun, had been visiting the west since the early 1830s - Stewart in fact had all of his gear, including his Mantons, stolen by the Crows in the mid-1830's. George Ruxton, another Engishman, visted the SW USA in 1846 and was also armed with British made double guns. both rifled and smoothbore.
In the 1850's uber rich sportsman Sir George Gore went on an extended hunting trip with Jim Bridger as guide and had an arsenal of finely made guns.
Gore's entourage included his valet, a dog-handler and a pack of thirty-two greyhounds and eighteen foxhounds, a fly-tying specialist (who was constantly gathering new material for artificial flies), and attendants who cared for Sir George's arsenal: seventy-five rifles, more than a dozen shotguns (all muzzle-loaders but one Sharps rifle) and many pistols, including a number of revolvers. Captain Randolph B. Marcy, U.S. 5th Infantry, who gained fame for his role in the Utah Expedition of 1857-58, met Gore soon after his return from the mountains and "observed the names of Joseph Manton, James Purdey, Westley Richards and other celebrated makers" on his guns. All were fully engraved and fitted with carved English walnut stocks.
http://historytogo.utah.gov/salt_lake_tribune/in_another_time/021697.html
John Palliser, another Brit, was a hunter for Ft Union in the early 1850's and recommended doubles, either smoothbore or belted ball rifles, as the best type of gun for western hunting.
Yep our perceptions have often been colored by Hollywood, but sometimes truth is stranger than fiction.