I am sure that rifle has sentimental value, which cannot be insured. As for dollar value, I don't think it would be worth any special insurance other than being covered in your standard home insurance as personal property.
It is what was called a "Flobert rifle", after the French inventor. Most imported here were made in Belgium and sold in the 1880-1910 era for $3-4 (a Colt SAA was $16). The first ones had no breechblock at all, depending on the mass of the hammer to keep the fired case in the chamber until the pressure dropped, and yours appears to be of that type. Value today is around $100 solely as a curiosity. Despite its age, there is little or no collector interest. Many gun shops will not sell those guns or take them in trade since the liability risk is too high.
I STRONGLY recommend against firing it, as modern cartridges are higher pressure and the empty cartridge case could come back into your eye.
Jim