I think you will find that it is a rare Manufrance gun built after 1885 that has damascus barrels. I know for fact that this is the case with Darne guns, the 1894 patent R was never available with damascus barrels. The previous examples I've handled, including an 1870s vintage prototype R, were all steel barreled guns. The sliding breech guns started with brazed steel barrels and the grades higher than Halifax got monoblock barrels around the time that proof with powder T came into use-1900. There were several grades of Halifax, at one time, and monoblock barrels were an option on the higher grade.
I have seen a model A Darne pivot breech gun with damascus barrels, that design was patented in 1887, but, was likely in production earlier, maybe much earlier.
Best,
Ted