Need help to identify this firearm

[Longrange1]

Have inherited an old purportedly 44-40 single-shot firearm. '
29.5" barrel of which first 9.5" are octogonal.
Smooth bore. Outer barrel diameter 0.625" at end of octogonal section tapering to 0.53" at muzzle.
Belgium stamped on bottom of barrel just in front of forestock.

[Mainspring]

.44-40 does not sound quite right. Do a search for "Belgium Flobert" and quite a bit should show up. This will be a large category, relatively inexpensive guns, many without a makers name.

I'm not sure your rifle is in this category but images seem to place it there. See if yours is centerfire or rimfire, that might help figure out what you have.