No one is going to literally take away anybody's car. They will increase the price of using one so much as to make it impossible for poor people to keep their cars.
If you properly price an externality, the free market will help you deal with it.
It can be in the form of direct support of various activities of the petroleum industry, such as drilling, refinement and pipelines in the name of creating new jobs, but also in giant infrastructure projects reserved for cars, and legal requirements of square meter prices for car parking many orders of magnitude below market cost.
It was the way post-war society was built up and will take a very long time to change. It's so entrenched that once you start seeing it, it is really everywhere.