This is almost certainly a Spanish pistol, from Eibar in the Basque region of Spain. The French company "Unique" was started in the French Basque city of Behobie (about 50 miles from Eibar) in the 1920s by a Spanish gunsmith from Eibar, Jose Uria. This company moved to the nearby French city of Hendaye in 1928. At this time the legal name of the company was "Manufacture d'Armes des Pyrénées Françaises" (or MAPF), and "Unique" was a brand name for the 6.35mm/.25 vestpocket pistols it made (the Unique model 10 and variants).
MAPF was an outgrowth of an earlier company in Behobie called "Uria & Arenas Frères" (Uria & Arena Brothers), founded in 1923. The Arenas brothers -- Modesto, Isadro and Gregorio Arenas -- were members of an gunmaking family in Eibar. In 1921 the Eibar company "Barrenechea, Gallastegui y Arenas" registered (in Spain) the name "Unique," along with the logo of a lion in a rectangle (later changed to an oval), and began producing 6.25mm/.25 vestpocket pistols similar to yours, with the curved serrations on the slide. It continued to make "Unique" pistols for a number of years, although the name of the Spanish company appears in the 1928 Spanish "Census of Arms" as "Barrenechea y Gallastegui." So the French and Spanish "Unique" pistols are closely tied together, and were being made at the same time for awhile.
Check the frame (especially the left and right sides of the rear tang), slide (rear) and barrel carefully -- they will typically have Eibar proof marks that may indicate the date (although the manufacturing year mark was not used until 1927) and maker. "BG" was the maker mark for "Barrenechea y Gallastegui". Without the proof marks, dating these more than generally is very difficult -- as a Spanish pistol, it would date to the 1920s or 30s, but no later than the Spanish Civil War. The curved serrations strongly suggest the 1920s. Where on the frame is the "2088" stamped?
Eventually MAPF changed its name to "Unique" (after WWII, I believe); in later years (1970s+) it focused primarily on making high-end target pistols and rifles that still sell for quite a bit (often $1000+). Unique went out of business in 2004, although one of its rifle designs is still being manufactured by a German company (see the "Unique Alpine" at unique-alpine.eu, or just Google it). Prices start at about $5000, and they are not sold in the US.
According to Zhuk's Encyclopedia of Handguns, the Spanish company "Unceta y Compania" (better known as "Astra") also made .25 Unique vestpocket pistols with curved serrations for MAPF in the 1920s (see entry 37-216 for the "model 1924"), although I am not sure how reliable this information is regarding the maker. Astra normally placed the gripscrews in a different location (center of the grips), while your's and where Zhuk's illustration show them are where Unique (both Spanish and French) located them (rear edge of the grips). Astra is known to have made pistols for the French gunmaker "Union," which is sometimes confused with "Unique" (it made some very similar pistols at the time). But there was a lot of parts trading between the many Eibar gunmakers back then, and apparently some between the Spanish and French Basque gunmakers.
Are you sure that this has a 5-round magazine? I don't think any of the French Unique pistols based on the model 10 (ie, models 10, 11, 12, 13 and 14) held fewer than 6 rounds (some held more), and none of the Spanish vestpocket Uniques I've seen do either. The magazine may be faulty, or may even be from a different pistol (not uncommon -- almost all the Spanish and French vestpocket pistols of this period are very similar (Browning 1906-derived) and magazines from one pistol often end up in a different one). If I recall correctly, I can swap the magazines from my 6.35mm/.25 (Spanish) Uniques, (French) Uniques and (French) MAB As (all from the 1920-30s) without any problem, although the magazines from some other vestpockets look almost the same but will not quite fit (but could be made to with a little fitting). Given that this was painted black at some point, and the grips are obviously not original, some previous owner may have replaced the original magazine.
Originally Posted by Moparkid13
My father in law gave me one a few days ago. It was spray painted black and very dirty.. I have it stripped so far and cleaned.. I'm trying to do some research on it and it's very similar to the model 10 but with some differences.. It has 5 round magazine, the 10 is a 6 round.. Also it has curved slots on the slide and the 10 has straight slots.. I cannot find 1 like this one at all on the net..the slide reads--
"Unique" Modele Cal. 6.35
The frame has 2088 which I'm assuming is the serial number