Hi Guillaume, and Welcome to Firestryker!
Yes, you can buy pre-made barrels, and as a re-enactor with over a decade of experience with black powder in reenactment, and a target shooting enthusiast with blackpowder artillery and hand weapons of almost 30 years experience (28 - I was 12 when I fired my first full-scale artillery piece), let me strongly recommend, for both your own welfare and safety, and the safety of those around you that you buy a pre-made barrel by a reputable gunsmith - even if you never intend to shoot anything other than blanks.
Here are some blackpowder gun part suppliers
(You can buy seperate barrels and locks from the Rifle shop. They have two early 15th century handgonne kits that aren't as advanced as the one you like, but were still in use to the 1460's or '70's, and they have parts for an Early English clavier that has a pre made barrel you could modify, and a sprun sear lock you can modify as well) http://www.albion-small-arms.freeserve.co.uk/home.htm
(Albion has a lengthy waiting list and isn't taking custom orders right now, but I bet if you were to e-mail him, you could buy a barrel or a lock off him)
I believe you can get gun parts from your fellow Canadians here - http://www.loyalistarms.freeservers.com/index.html
Check this page out, it shows a number of extant handgonnes and arquebuses, including drawings of early firing mechanisims. Also note just how long simple barrels strapped to stocks with no lock at all persisted - right alongside the more advanced forms. Early 16th century detailed art showing Landesknechts shows arquebusers applying match to touch hole by hand. See how late very crude seeming haquebuts that look like a tube with a rod protruding for a stock persist. There are photos of Swiss guns in Swiss museums from the time period you seek, as well as drawings from Diebold Schillings history of the Burgundian wars (later than the wars) showing different types of guns employed by the Swiss and Burgundians.
Another page devoted to 15th century blackpowder weapons. http://www.xenophongroup.com/montjoie/gp_wpns.htm
A Forum devoted to pre-flintlock guns http://www.muzzleloadingforum.com/ubbthreads/postlist.php?Cat=0&Board=preflint
A webpage telling you how to make slow match for your gun http://www.metamuseum.com/us/slowmatch/index.cfm?&PlaySounds=no
I would be remiss to not point out almost the exact gonne you wish to hav is available through Historic Enterprises
I hope this gets you started, and if you will be reenacting with us, I look forward to seeing you in the field!
If you have any questions at all, please keep the thread going!