Looking through Dixon's "European Sporting Cartridges" volume 1 does not show any 3 inch (72-77mm) straight cartridges with bullet diameters between 10,75mm and 12mm. Fleming's "British Sporting Rifle Cartridges" shows only a single undated entry for an early coiled .450 at 3 inches, but nothing in drawn brass at that length.
There is the pre-1880 U.S. .45 2-7/8" Sharps cartridge, but it seems unlikely that a Francotte double rifle built around 1912 would be chambered for that round.
An interesting puzzle...
