Angel:

Rusty forwarded your pictures. "B. Plomb" means a rifled barrel intended for lead bullets. "B. Blindee" means a rifled barrel intended for jacketed bullets. .450 Nitro Express cartridges were loaded with jacketed bullets and .450 Express (black powder express) cartridges were loaded with lead bullets, usually paper patched. Thus, I believe your rifle to be a .450 Black Powder Express. Do NOT fire .450 Nitro Express ammunition in it.

The chamber cast suggestion is a good idea. The proof marks would be the same for the .450 3 1/4" BPE, the .500/.450 3 1/4" BPE, the .500/.450 No. 1 BPE, etc. The .450 3 1/4" BPE was the most common and since it fits the chamber, that is probably what it is. Never hurts to check though.

Have the rifle checked over by a competent gunsmith. If it is safe to fire with blackpowder loads, it is safe to fire with smokeless black powder equivalent loads (nitro for black). Loading data is available.

The Francotte rifles were ususally of excellent quality. In good working order, a .450 BPE double would make a perfect boar rifle. I certainly wouldn't mind inheriting a rifle like that.