The 8th arrondissement at lunch time has a uniform, distinct from La Défense's. The 16th's rue de Passy and the 7th's rue Cler have clear differences in clothing and speech style on a Saturday morning. Le Marais and the 11th have different stereotypical accessories.
We'll see what'll be the public opinion about us in 108 years!
The world wasn't bigger back then (or even today). People were less connected and their speech patterns were not influenced by audio-visual media.
I don't think I can spot accents from different parts of Paris, but I can definitely spot accents from different parts of London.
I think there's something else at play, I'm not sure what. Maybe how much people have moved in last few decades? Maybe how much of a hyper-local life there is in each area?
(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.