Since your "free market" is a theoretical construct, more or less, let's do a brief thought exercise to see how it relates to the state, and why the state is a
necessary element for capitalist property relations to be upheld.
1. Let's assume a group of 100 people with "no government" to start. There are 5 factories. Somehow (

I'll let you fill in how this happens since you don't want to consider primitive accumulation through slavery, genocide, etc.), 5 people of those 100 come to "own" those factories. 85 people are employed in those factories and 10 people are unemployed.
2. For simplicity's sake, let's say there's a 12-hour workday (no 8 hour workday without labor struggles and the resultant legislation

) and the workers produce 1 widget per hour. Each widget is sold for $20. Each worker is paid $2 per hour (no minimum wage without a government

. Let's assume this is the minimum for workers to be able to also purchase goods over some time period). The worker's labor generates $240 of revenue for the firm per day, but he or she receives only $24 in compensation. They don't receive the full value of their labor - the owner takes the $216, covers operating costs and whatnot, reinvests some to expand his enterprise and/or pays himself (both of which adds to his personal wealth and power

).
3. The workers realize they are being exploited. They are being essentially robbed of $216 every day. They find it difficult to survive and hold little power over their own lives since all they have to sell is their labor.
4. The workers make a move to establish more just relations and seek to operate the factories on a communal basis and get rid of the owner, or simply share everything evenly.
5. Seeing this threat to their wealth and power, the owners use their capital to hire armed men to suppress the workers and maintain the current distribution of resources. Every time the workers make a move to operate the factories on a communal basis, these armed men terrorize them into submission with weapons.
6. With this ever-present threat from the workers, the owners institutionalize an armed force and establish apparatuses to mitigate conflict with the working class. The armed force and other apparatuses enforce contracts and property rights, among other things, which also help mitigate conflict between owners. These things establish rules and owners can grow. Otherwise, one owner could just try to hire enough armed men to take everything from the other owners, too.
7. With an armed force (police/military/etc.) and bureaucracies to suppress and/or mitigate inter-class and intra-class conflicts, we now have a state. Its purpose is to maintain the existing distribution of resources between the classes.
8. Perhaps over the course of state development, voting opens up and workers agitate and get some reforms passed. Maybe some social services begin to be offered by the state. These have the effects of giving the state a more legitimate appearance and deflating worker agitation. This is all to perpetuate the system and save it. (on a side note, Keynes was often lambasted by conservatives as being a socialist or communist

. He himself noted that he was saving capitalism with his policies, not undermining it. The state is an arena where class conflict is managed.)
Capitalism requires a state. Otherwise everyone would see how they're getting screwed and would take over the means of production (then there's no more capitalism). What stops or delays that? State force. Which is deployed on behalf of one class (the bourgeoisie) and against another (the working class).