“Gunslinger” is largely going to be after 1865, after the US Civil War. Revolvers as we know them in the old west only existed after the 1850s. The first revolvers that you would call a revolver would be about 1835. So you don’t really have the overlap for French privateer, unless it’s a former privateer.
Cool idea, except the pirates wouldn’t be part of it cuz the era you’re calling the “old west” didn’t start in 1800 - westward expansion was in its early beginnings then. The classic era of gunslingers and saloons and stuff was really a very brief period between the Civil War and the 1890s. Another forgotten bit of trivia about that time is that around 25% of cowboys then were black.
Or you play a system that has build a world where the age of exploration, king Arthur, the Russian revolution, the hanseatic league, the itialian city states, the spanish inquisition, and much more are all happening at the same time.
7th Sea has some wacky world building, but it stays realistic enough to be quite believable and coherent.
I was going to guess Rifts because I’ve heard crazy things about their setting, too.
There were gentleman thieves in the west too https://en.m.wikipedia.org/wiki/Black_Bart_(outlaw)
[off topic?]
“Red Sun” Toshiro Mifune and Charles Bronson. After bandits steal a sword being carried to Washington, a samurai and a gunslinger must unite to bring it home.