The rifle is a Warnant action, an improvement on the Flobert. The original Flobert action, which dates to c. 1845, had no breechblock, and depended on its large and heavy hammer to keep the pressure in the chamber when the cartridge fired. Later, Warnant added a breechblock in the form seen here, making rifles that were stronger and could use more powerful cartridges.
Flobert invented the rimfire cartridge, an idea that was later used by a couple of guys named Smith and Wesson.
Those rifles and pistols were made by the ton in Europe, mainly in Belgium, and many were imported into the U.S. before and after WWI. Most were utilitarian rifles for plinking and hunting small game, but some were at the high end with elaborate engraving and intricately carved stocks.
They were made in calibers from 6 to 9mm, including 9mm rimfire shot; some stronger ones were made in centerfire for moderate power rifles and even conventional size shotguns.
Look on the side or bottom of the barrel and breechblock for an oval with the letters E L G. That is the Belgian proof mark and would confirm that it was made in that country. If that is not present, a picture of any markings that are there might help determine its origin.