On the other hand Paris proper (where those height restrictions apply) is already one of the densest cities in the world, along with some of its suburban cities [0].

I think around these parts there are two separate problems:

- foreign/1%er investors buying up property and leaving it empty. Across central Paris ~20-30% (depending on districts) of homes are empty [1].

- The city is geographically too small, being locked inside the area of its mid-19th century fortifications, replaced in the 70s by an urban highway. This makes most of the land (and homes) outside of this circular highway much less desirable and therefore a lot less dense. If the suburbs were built as densely as Paris proper, most of the people living in the metro area would be able to live in a space a tenth of the size, avoiding so much commute misery.

[0] https://en.wikipedia.org/wiki/List_of_cities_by_population_d...

[1] https://www.terraeco.net/A-Paris-toujours-plus-de-logements,...