As a person with SUV and big family in Paris, I suggest we do the same with obese people and public transport - now that my kids will need to use it more frequently while paying more for sq ft.
An interesting intersection of gov trying to encourage families could be used here to offer a tax-relief on people that carpool (which'd by default therefore include families)?
At the end we got rid of our car and not planning to buy another one. For those occasions that happens 1-2 times a year, we just use a car sharing app. It's also a lot cheaper than maintaining a car.
Buses do tend to be a bit easier if you're travelling outside of peak hours. Otherwise, you might have to let a bus or two pass you before one comes with enough space for the stroller.
Things are supposed to be a lot better with the Grand Paris Express, although that won't help much intramuros.