There were several variations of .32ACP Unique pistols made by
Manufacture d'Armes de Pyrenees of Hendaye in France. They are all based, to a greater or lesser extent, on Browning designs and because the pocket-style Brownings had the magazine-release in the heel of the butt, a nine-shot magazine won't work in a gun designed for a seven-shot magazine, or vice-versa.
The first of the Browning M1906 copies in .32ACP, was the Model 15 with a six-shot magazine. The Model 16 was the same, but had a seven-shot magazine. The Model 17 was again broadly similar, but had a nine-shot mag.
The Model 18 was based on the Browning M1910 with a six-shot mag. The Model 19 was the same except with a seven-shot mag. The Model 20 was the same but (you guessed it) took a nine-shot mag.
During the war, when the Germans took over production, they put the Model 17 (with the nine-shot mag) back into production with the grips marked "7.65mm 9 SCHUSS" and about 50,000 were made. They later modified this with a more rounded back to the butt and an external hammer to form the "Kriegsmodell". Some have German military acceptance marks, some do not. The nine-round mags should be interchangeable.
After the war things get a little more complicated, so since it was a WW2-era gun, I won't go into it (breaths a sigh of relief
).
In summary then - you'll need to know the magazine capacity of the gun in question. I suggest finding out the model number and asking around some of the antiques and militaria websites. I don't think you're likely to find parts in a regular gun store, though.
Best of luck!