If you draw the border of Paris further and further out, I’m sure you can get the density as low as you want. Meaning: the density figure of a city says very little of how dense it is and says more about how far out into sparsely populated farmland the official city limit ends.
Go look at a Google street view of the far ends of Stockholm metro area…
Paris has a population density of 9,800/sq mi across 1,101.7 sq mi and an inner core of 53,000/sq mi across 40.7 sq mi.
Stockholm’s urban area of 11,000/sq mi across 147.35 sq mi, is comparable to Paris, but it’s inner core 73 sq mi is a much lower density 13,000/sq mi. Even if you assumed all those people lived in a 40 square mile “inner inner” core you still don’t get close to 53,000/sq mi.
Go look at a Google street view of the far ends of Stockholm metro area…