This is the Belgian 1777 model, copied from the French. This is the same as the one at the start of the thread, except that one has had Swiss arsenal numbers added and the cantonal mark made on the stock.
The gun shown here is purely Belgian.
http://gelain.net/fr/node/19
As noted elsewhere, Switzerland was not manufacturing her own arms at this time and many cantons used existing stocks of French weapons left from Swiss involvement in the Napoleonic wars, or some cantons imported the affordable Belgian weapons.
In an attempt to bring some order to the situation, the Ordonnanz 1817 sought to define the specs of what were essentially 1777 muskets.
This is what I have picked up along the way, I'll try to add some references.