I know John Browning was great at designing firearms, but it seems strange that a European firearm company would "commission" someone, instead of just having their own engineers design it.
Browning had quite a history with Fabrique Nationale. Browning made a living by selling his designs to companies, and FN was a customer of his well before the Hi-Power came around. The M1900, M1903, M1905, and M1910 were all Browning handgun designs manufactured by FN (the 1903 and 1905 designs were also sold to Colt), as was the Auto-5 shotgun.
Browning had done a lot of work with FN in the past, especially at the turn of the century when he stopped working with Winchester and looked to FNH and Colt. Look guns like the FN 1900, 1903, etc. All are Browning's designs.
IIRC it was actually the French who were looking for a new gun, and FNH had to design a pistol that was relatively small, had a manual safety, a magazine disconnect, and held at least 10 rounds of 9mm, if they were to get the contract. FNH, in turn, commissioned Browning to design the pistol, which he did a lot of, but had to work around patents and whatnot due to his 1911 rights now being owned by Colt. He did the bulk of the work for the Hi Power, but he died in '26, which was 9 years before the design was finalized and adopted by the French. FNH were the who finished it, but IMO, ruined the gun, mainly by turning a striker fired gun into a single action hammer fired. If you've ever shot one, you'll understand what I'm talking about. The magazine disconnect doesn't help either.
Have you tried this question over at /r/guns? Might have better luck