There's nothing about disallowing private ownership of the Earth's common resources, natural monopolies, etc. that stops having free markets everywhere else.
If anything, allowing that is what corrupts free markets - as even with privatisation, you never have a real free market on the railways, highways, or electricity grid because we can only build a limited number of them and can't support multiple disjoint networks. But those corporations can then use that captive market for an unfair advantage entering other markets / verticals.
I think the best solution would be free markets and liberalisation, except in natural monopolies, and a lot of taxation against accumulated and inherited wealth (not income) to provide a level playing field and economic mobility.