In my experience, cars are discouraged from city centres, but not banned. You can drive your car all around Amsterdam, although you’ll have many one way streets and parking is going to very expensive for non-residents… and it’s hard (but not impossible) to find street level parking. Amsterdam has a number of car parks in the outskirts that are cheap if you can show that you used public transport afterwards.

The result is that people use their car (if they have one, still quite common esp. for families) to get out of the city, or big errands, but use bike or public transport for day to day trips.

Actual car free zones exist in cities across Europe but tend to be pretty small and constrained to the hyper centre, like the church square and the major shopping streets. Not that I’m opposed to them being bigger but that seems rare at this point.