Mr. potato:

I have not been inside a Hotchkiss, and I can't say that I know anybody who has. It is entirely possible that it is the second ugliest rifle ever made. Cool.

From your description of the problem I would assume that the sear is not engaging the firing pin, cocking piece or whatever it is intended to mate with. This could be the result of something as simple as dirt or debris in the sear notch which is limiting sear engagement. Another possibility would be a broken sear spring which is not pushing the sear up into engagement. This could be the same as the trigger return spring, but I am just speculating not being familiar with the workings of the action.

Anybody been inside one of these? Now I be curious...

Glenn