As I recall, without digging through books, Mr Browning designed a 9mm at the request of FN who had a RFP from France. Browning and Saive at FN kicked the basic design around a while and produced a finished gun called the Grand Rendement. The French turned it down.
Mr Browing passed away but Msr Saive kept fooling with the design, including plowing Colt-Browning 1911 elements back in as the patents ran out, eventually delivering the Grand Puissance we know as the High Power, first adopted by Belgium in 1935.
In the meanwhile, the French took some of those off patent ideas, added the Petter package lockwork, and came up with their 1935A. It is often said that the caliber was based on the .30 Pedersen Device cartridge. That is kind of hard to see, the Pedersen Device was never deployed and the round not otherwise used. Maybe a French ordnance expert saw one of the Pedersen Device demonstrations late in WW I and liked the round. Who knows for sure?
FN hurredly ran up a prototype in 7.65 French but there was no interest, the French already having their own in-house gun.