What you have there appears to be the 'Kavallerie Karabine' version of the Mauser C96 pistol. That particular variant was was produced in rather limited numbers, but saturation of rare and barely utilized guns is about par for the course in BF1, so shouldn't be unexpected! It was a German made weapon, and one of the first examples of a semi-automatic pistol to go into production (guess what year!).

The big wooden stock which gives it the nickname "Broomhandled Mauser" on the back is detachable on many models of the C96 (but not all), and actually doubled as a case, as demonstrated here. The forward grip under the barrel helps to differentiate it from other models, some of which also came with the 'Broomhandle', but is indicative of the Kavallerie Karbine. Here is a picture of the real Kavallerie Karbine, and a Pistol Carabine for comparison. If you want to see how it worked, you can check out this video by /u/othais which provides an animation of the internals in action at the time stamp (and provides some footage of the gun in action too)