You’re right FOX News is anti-American. Their commentators have encouraged Americans to boo the US soccer team. They have supported the death of Americans with their anti-vaxxers propaganda. That seems cut and dry.
Technically, FOX News is American-owned but that’s because Rupert Murdoch has acquired American citizenship. But he’s originally from Australia. BTW, the Aussies don’t like Murdoch much. Also, Carlson and most of the other talking heads on FOX News are commentators, not journalists.
There is a big difference.