Yeah, most European countries have what's known as "Social Market Economy" which is based on the free market. It's basically impossing socialist laws without changing ownership, just putting limits to the private hands. Because in the end it doesn't matter if the means of production are privately or socially owned as long as some social limits are impossed .This prevents huge monopolies from raising up and killing the small companies (in a way, protecting social welfare is the best way to protect capitalism).
Sadly, because US does not care so much about protecting social welfare, huge international companies based on the US rise up to eat up market, mess up with the competition internationally and more than once have clashed with the antimonopoly laws in Europe, or have to conform to things like the GDPR and other European social laws.
The fear the US has to socialism seems to have creeped into any kind of social reform, and any mention of social measures often gets automatically identified with communism as if they were equivalent. There's the irrational belief that it's impossible to have any form of social reform that doesn't lead to authoritarianism, and when presented with any possitive influence social reforms have had in any country (even in the US) they'll immemdiatelly attribute it to capitalism, or justify it saying that it's still capitalism, without acknowledging that it's thanks to those social reforms that capitalism (and economic competition) was healthy.