I don't disagree. That still exists to some extent. I don't think I could tell a Brooklyn accent from a Bronx accent, but i think some can? (Can they hear it in 20-year-olds not just 60-year-olds? Not sure).
(For context: I did not grow up in NYC, but my family was from there, and I lived there for quite awhile myself as well. It's entirely possible someone who did grow up in NYC can do better than I can, but, at least to my ear, it gets very close to just standard American broadcast English the younger you go, so I doubt it.)
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.