The FN Model 1903 was a Belgian-made scaled-up version of John Browning's model 1903 pocket hammerless pistol. The pocket hammerless was made in .32 ACP and .380 calibers for (primarily) the civilian market in the US by Colt, and the FN model was chambered for the more powerful 9x20mm Browning Long cartridge, with military and police contracts in mind. The most common source of the FN pistols in the US is from the Swedish contract for the guns, but they were sold to a number of other nations as well.
This example is from the Russian contract, which included shoulder stocks with the pistols. Many military automatic pistols from this time were offered with the option of combination holster/stock units, which could be used to provide improved accuracy to the shooter. The stock for the FN 1903 is a bit different than most, in that it requires the use of an extended 10-round magazine instead of the standard flush-fit 7-rounder. As with most such original guns, these have been specifically exempted from NFA regulation in the US.