A flintlock ships or cavalry musketoon (carbine). I'm thinking a .69 cal 1777 French Cavalry Carbine - when the first carbine is taken out of the crate, you can see the underside and obverse - the brass fittings seem to match, as and lefthand side (obverse of the lockplate) seems to show a bar and ring that also matches the 1777 carbine.
I'm not sure why the filmmakers went with that particular musket, but its fairly available as a repro.
Gee, I've wanted to use the word musketoon in a post all week
Mission accomplished, and one of my favorite sounding words.
Musketoon.
The episode is online - scene at around 18:58
https://www.youtube.com/watch?v=GCnayRFj-2M