The Flobert was both a brand, and a style of action. A VERY weak style. Which was OK, because they were PARLOR guns- indoor target shooting. Think pellet gun, without the pumping. They were made in several calibers, up thru 9mm.
Now here is the important part- the weak action did not matter, because they shot an extremely weak cartridge. No powder. Primer only. A cartridge with powder will wreck the gun, and it won't do you much good, either.
BB Cap stands for Bulleted Breech- it was a percussion cap, with a lead ball press fit in it. I have single rounds in 4mm, 6mm, .22, 7mm, .32, and 9mm. No, other than the 6mm and .22, not made any more. Older than the .22 Short.