Just so we're talking about the same scales, the 133 miles of the Paris Métro rapid transit system covers the entire Paris metropolitan area[1], which itself has a population of around 12.4 million residents[2]. NYC's population across the five boroughs covered by the MTA is around 8.5 million residents[3].
The last cost projection for the Paris Métro expansion[4] for 120 extra miles of tracks, stations and lines is roughly $25 billion.
If anything, this clarification only further reinforces your point that, even taking into account a hypothetical 5x cost overrun, Paris would still come out ahead from a $/mile metric.
[1] https://en.wikipedia.org/wiki/Paris_M%C3%A9tro
[2] https://en.wikipedia.org/wiki/Paris_metropolitan_area
[3] https://en.wikipedia.org/wiki/Demographics_of_New_York_City
[4] https://www.theatlantic.com/magazine/archive/2016/03/tying-p...