What is with the 3 indents on the breech break on mine?Flobert has become something of a generic name for simple breech loading pistols (some long guns too) but a true Flobert has no breech closure. The cartridge head is open to the world until the hammer falls. In place of breech blockage, it has a massively heavy hammer that has the firing pin as a part of it. The heavy hammer provides breech closure for its very low powered cartridge.
Yours is primitive breech loading pistol of break open design, probably as others have said, intended for indoor amusement shooting.
There were countless designs & configurations by as many makers in mid 1800s which makes ID & source unlikely. Yours probably once was a handsome piece, considering the detail of its stock, etc.
Here's another one the same comments apply to except it is percussion ignition, barrel breaks down & the little breech block bearing the nipple hinges sideways. I was probably best to shoot the .31 cal perc paper cartridge.
In his next to last picture it shows the barrel face and there are 3 indentions there. Imagine a .22 Rimfire being dry fired and the firing pin left marks on the barrel.Not that I might have the answer but I don't ID your meanings of '3 indents' & 'breech break'. Maybe I'm lacking something but I can't see 'indents' or 3 of anything.
I have messed with that and it does indeed adjust trigger pull.I haven't seen the set-trigger mentioned, which further confirms its quality & intent for target shooting. The little knob just behind the trigger with cross-drilled holes is for adjusting the trigger sensitivity.