I'll go against the flow here. I do agree that I would be hesitant to shoot this particular rifle due to rarity and condition. However In the mid 1800s French metal work was some of the best in the world. I'd not be concerned about the design of the rifle or quality of materials and/or workmanship. Warning: These comments are meant to apply to a rifle of this design in general, not your particular rifle because I've not actually seen your rifle.
Paper cartridges' for muskets and rifle muskets were of sturdier construction than those made for handguns. In my experience paper cartridges for muzzle loading muskets or rifle muskets were made one of two ways. Either tapered towards the back so that when the cartridge was loaded completely the paper tore exposing the powder or the cartridge was torn, powder poured down the barrel then bullet and wadding rammed down on top of the powder. There was too much risk of the flash from a fouled nipple not igniting the charge otherwise.
This rifle should have a rough spot on the face of the bolt to tear the back of the paper cartridge. It may also have a tapered chamber or be designed that the projectile rests against the rifling so that the back of the cartridge, with proper powder charge, is held firmly and in proper position to tear. In theory a loose powder charge could act the same as a ball not seated all the way down onto the powder charge in a muzzle loading rifle and actually cause more chamber pressure. Remember though there were a couple variations of this trial rifle and the spot intended to tear the paper might not have been on the first variation.
In my opinion, the risk to a rifle of this design IN GOOD WORKING ORDER is in not properly cleaning it after shooting. Not in the shooting of the rifle itself with proper load. Remember, the last person to actually fire this rifle was probably trained how to correctly disassemble and clean the rifle by the French Army in the mid 1800s. And a strong YES to normal shooting precautions like shooting glasses and hearing protection. There were very good reasons Napoleon III discarded the the idea of paper cartridges in the trial guns and the French adopted a a very similar rifle that used a metallic case.