For refence, here is the interaction in the game
I'm wondering why a police officer would care whether a black person was smoking in the early 1900s and the significance of using the term "gendarme" instead of "police officer", "copper", etc.
Is it deeper than just gendarme as a term for policeman?
Before Booker speaks the janitor says, "Someone gave it to me, I promise. I ain't never smoked one before." Based on the wording I would guess that was a marijuana cigarette. As for why Booker uses the word gendarme instead of police officer maybe someone else can answer that.
It might be a reference to French or Creole language and culture you might find in the gulf, in places like New Orleans. But there's no real indication Booker has spent time there.
He's basically saying "don't worry man, I'm not a narc" after catching the guy smoking on the job. Something he would have been severely punished for
Not sure how this holds up in other countries, but in Belgium the gendarmes were a sort of military police (as in a police force, but officially military), so they were known to be more strict and they were also the guys to be called in to break protests and strikes and such.
"Gendarme" is one of the french words for police officer and large parts of the game have to do with France. shrug