The per sqm cost varies widely by neighbourhood and quality of the apartment. In my Brooklyn area it's a lot cheaper than that. Based on a mental calculation we're talking very roughly around $20-$25/sqm/mo. That's on the expensive side for Brooklyn but definitely not the most expensive. By Manhattan below Harlem standards that's very cheap - there you pay about double that, again with considerable variability.

By comparison what would rents be like in a nice but relatively poor but gentrifying and very non-white outer arondissement?

That's 8 euros per square meter per month...