Paris: 55,673 ppl/sq mi
New York City: 27,016.3 ppl/sq mi
San Francisco: 17,179.2 ppl/sq mi
Zurich: 12,000 ppl/sq mi
Vienna: 11,205 ppl/sq mi
San Bruno: 7,505.0 ppl/sq mi
Mountain View: 6,034.8 ppl/sq mi
San Jose: 5,256.2 ppl/sq mi
Cupertino 5,179.1 ppl/sq mi
Menlo Park: 3,271.3 ppl/sq mi
For instance your figure for Paris is only the actual city of Paris, which doesn't include its own suburbs: it's really just the center. The subway extends a fair bit beyond the actual city boundaries. As an example "La Défense", the business district of Paris, isn't even inside Paris.
So of course it's very dense. The equivalent for NYC would be Manhattan without the 4 boroughs. Maybe even a subset of Manhattan.
The density of the Paris Urban area--which is about 1/6 the size of the Paris Metro area but about 20x the area of the "City"--is about 10,000/sq. mi. (10m people in about 1,000 sq. mi.
If San José replaced all its single family houses with 3–5 story apartment buildings, the density would increase 5x.
They exist and they tend to be eyesores hidden behind trees. The tell-tale sign is the parking found underneath the living level exemplified with non-structural walls. So yes, it's even worse than I stated. Land is grossly underutilized for a city the size of sanctus iosephus. We can blame proper suburbs like MTV, Sunnyvale, &c, but S. Joe takes the cake. It's a city, at least on paper, and should act like one.
(Not that the other parts of San Jose are any better.)
As an historical note, the key planner/city manager from San Jose came from the Los Angeles area - Hamann ( https://en.wikipedia.org/wiki/A._P._Hamann ). For twenty years (1950-1969), he did his best to make San Jose a sprawling city that sucked up as much of Santa Clara county as he could make happen.
There is a lot of books on what makes city good place to live this days on. I found it fascinating (as SWE).
For example, a city can zone land to be high density residential but that doesn't necessarily mean that people who live there will sell their low density houses so that they can be redeveloped.
A high density area can "want" a public transit station, but the transit authority may not have the funds, or the motivation to give them a station. And there is no means for a city government for "force" them to.
Instead, we're left with the "master plan" system which is a living document that the city government maintains which expresses a "vision" of what the city would like (their plans) and the city council signs up to help make it real when there is something within their powers to do to help it.[1]
A previous example of how hard that can be is the "Coyote Valley" area in South San Jose that was going to be "anchored" in part by large campuses of big employers (Cisco was the headline client). But the dot com crash hit and Cisco never moved in.
A current example is the new Apple "spaceship" campus in Cupertino which is to far away from the train station and in a set of roads that don't easily feed or drain to the 280 interstate. [1] And part of that is the problem in Sunnyvale, the plan says one thing, and when councilmembers have voted to help implement it, it has irritated citizens who didn't realize that was what the plan said.
It would help a lot if the Caltrain would be improved with more rides and less street crossings. Then there should be more buses bringing people to the Caltrain.