I might be wrong but most people who live and work in Paris don't drive. They have great public transit and there's a huge walking culture. When I was in Paris the only large vehicles I saw where taxis.
Your impression seems correct. I haven't manged to get to Paris yet, but the numbers I found align with your experiences. From a transport in Paris article:
"Paris has one of the most sustainable transportation systems in the world (private cars are only 12% of the overall traffic)"
"According to a 2018 INSEE survey, a majority of Parisians (64.3 percent) use public transport to get to work. Only 10.6 percent commuted to work by automobile. 10.5 percent walked or used roller skates; 5.5 percent commuted by bicycle; and 4.4 percent commuted by motorbike"
The local residents use public transit or walk/bike for work. They likely do exactly the same for daily errands, shopping, and entertainment. That's how it was in Berlin, London, and Helsinki when I was in those cities and it's wonderful.
I own an SUV and I'd still vote for a parking tax on them. Or pay per pound, estimated of course. You don't want people deciding to go for the mega F-250s because they aren't subject to the SUV tax.
We have two: A Ford Explorer (really trying to get the money to get rid of it) and a Forester. The Forester is small enough that it wouldn't be triple pay in Paris, but the Explorer is a 3 ton brick. We had it because a few years back we still had six kids at home, but now that they're filtering off to college, we are desperate to downsize. We're being stopped because our city's public transit (yay US cities) is a shitshow and our workplaces haven't given us raises in years. Yes, we're looking for other work, but so far it's been tough to find things in our field, etc.
As soon as we can, that vehicle is being kicked to the curb. It's a terrible waste.
I drive a Jeep (the unlimited though, so the large one). Good..
I want to see a trend towards smaller 4wd's and other cars. And I seem to be the only larger car that can park within the lines too. And the height of my car is low compared to the people with Rangers or Dodge Ram's (and it is rare to see any of those actually towing anything). In my case, I run a hiking group, so really need a 4wd, but will probably be looking at something more economical and smaller, like a jimny
I was hit by a car once when I was on my scooter, and I was lucky it was by a small car..
And I feel larger cars like me should pay extra (and I agree with some comments saying to charge per additional weight). We have a toxic culture here where people are moving towards big cars just to impress others (along with the toxic nonsense that comes along with it), and this is the only way the culture will change