The usual caveat about Paris applies: the city of Paris is but a tiny core of the larger Paris metropolitan area (Paris: 2.1M people, Paris metro: c. 10M). Paris is about one fifth of its metro area, a city like NYC is about half.

A closer analogue to being able to distinguish accents from Montparnasse, Montmartre and La Villette would be to able to distinguish accents from different places in Manhattan.

I think even today there are substantial accent differences within the Paris metropolitan area (think Versailles vs le Marais vs Aulnay), but within Paris proper not so much.