It'd still be interesting to try this for Paris, but it's not an easy thing to draw accurately at all.
I think the term of city here would simply refer to all contiguous dense areas of the core of the metro. Say the entire set of districts properly served by the mass transit network and where all dwellers live in apartment buildings, or possibly in row houses, but of course that latter kind of housing is much less in use than condominiums or rental apartments over the actual dense core.
So, that would comprise the entire central city bounded by the périphérique, the beltway physically segregating Central Paris proper, and some suburban municipalities adjacent to it. A bunch of them, but not all yet.
To try to understand what follows, you need to know the inner metro area sprawls over 4 administrative territories called départements. Let's roughly take those as the counterparts of what a county is in the US to make it simpler.
Those 4 central départements are:
1 - Central Paris, that's both a municipality and a so-called département on its own.
2 - Hauts-de-Seine, west of it.
3 - Seine-Saint-Denis, north and northeast.
4 - Val-de-Marne, south and southeast.
Wait, here's the Paris region.
https://aghg.wordpress.com/2011/12/0...france-schema/
Now you can recognize them more easily.
In fact, the real dense urban fabric of the core mainly expands to the west, over Hauts-de-Seine. Municipalities like Boulogne-Billancourt, Neuilly-sur-Seine, Levallois-Perret and just about all those of Hauts-de-Seine literally neighboring Central Paris are obviously some parts of the very 'city'. The dense fabric there is actually continuous, so in many cases over these areas, you don't realize whether you stand on the territory of Central Paris or in an adajacent town whose density is just the same. Most these Hauts-de-Seine so-called suburbs feel that way, fairly comfortable, if not desirable. Neuilly-sur-Seine I just mentioned is even downright a serious bit of a pretty large billionaire mile to the west of the city.
Things are very different and rougher to the east where most municipalities of the inner ring are still in the need of massive urban upgrades. Montreuil for instance, as pretty much everything in Seine-Saint-Denis.
Val-de-Marne is midway between Hauts-de-Seine and Seine-Saint-Denis. You could certainly call Vincennes and Saint-Mandé, maybe even Charenton-le-Pont the city proper, but not Ivry-sur-Seine or Gentilly in my opinion, cause they don't feel dense enough and are still a bit messy in their urban forms.
Um, bon, in a nutshell, you're only supposed to understand that the urban environment of Central Paris, hence of the city is expanding over the adjacent municipalities still called some suburbs, and that this process is yet much more advanced to the west side than it is to the east.
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