There doesn't appear to be a serial number nor a patent number associated with the forend attachment, unless the T handle is really worn. I wonder who Auguste Francotte's frame source or frame filer might have been.
Did not the use of rebounding hammers commence circa 1867?
This foreend/barrels/ action arrangement was already described in the book by Zimmer, "Die Jagd-Feuer-Gewehre", 2nd edition 1877, page 145, as "Variation III of the Lefaucheux action". No patent or maker mentioned.
Though J.Stanton, lockmaker of Wolverhampton, patented rebounding locks in 1867, they did not come into general use immediately, especially not on rifles. Due to the higher pressure of BP express rifles, compared to BP shotguns, and the then often weak primer cups, primers tended to flow back into the firing pin holes of rebounding firing pins and blow out or bind the action. Even Stanto himself continuedto make non-rebouding locks for express rifles. FI my .500 3" BPE hammer dr, Sold by John Rigby to a Mr.Heath in 1870, has non-rebounding locks signed by J.Stanton on the inside. Nor has my Birmingham made .500-.450 #1 BPE dr, dating to about 1880 rebounding locks.
BTW, the "LK" and "Gruendig" cartridges, though similar at first glance, were not "parallel developments". The LK numbers were black powder, lead bullet cartridges from the start, only post-1900 loaded as "nitro for black" with soft copper-jacketed bullets. The "G" cartridges were full Nitro, loaded with much heavier steel-jacketed bullets from the start, introduced post-1900.