I live in Paris and you can find highly specialized shops too. Some shops only sell about three types of fabric, some others will sell only buttons, a certain type of leather or a special type of ink.
I love getting in those shops and meeting the people who are really passionate about their visibly small yet huge niche. It always get wonderful once you start looking at the details.
FWIW, there is likely to be a button shop wherever you got enough seamstresses, tailors, dressmakers and fashion industry.
Buttons are really something you have to see and touch in person.
As a child, my mother used to take me with her to "Parker Buttons" in downtown Pittsburgh. I remember plunging my arms elbows-deep into containers of shiny black buttons. Nothing else like it in the world.