That term is an oxymoron.
In the USSR, the economy was controlled by the communist party on behalf of the workers. Under democratic socialism, enterprises are democratically managed by the people who work there.
...on behalf of the workers
We can define a socialism government to be one that have the goal of having social ownership and democratic control of the means of production.
We can define a free market to be one in which the laws and forces of supply and demand are free from any intervention by a government, price-setting monopoly, or other authority.
Thus a Free Market Socialism would be socialism which achieve social ownership and democratic control of the means of production by having a government that prevents price-setting monopolies.
Also you are avoiding the actual "social" side of the Socialism. In Socialism, there is always a forced redistribution mechanism in the name of "exploitation of the labor class". Which makes the "free market" impossible.
The state can naturally also create monopolies. patents are explicit in this, granting an entity a "limited" timed monopoly.
> there is always a forced redistribution mechanism
And now we enter the definition of terms. Forced redistribution is mechanism, not a goal in itself. Historically there have been governments that have tried it, through to be honest there hasn't been a country that have not had events of forced redistribution, and if the book Debt - The First 5,000 Years is correct in the historical data, the elimination of debt through violence was a recurring event that happened in all cultures. Forced redistribution happens all the time in history when the ability to repay get too impossible low compared to the amount of money being owned.
Perhaps my wording was not correct. What I mean by "forced redistribution" is getting money from producers by force (via taxation) and distributing it to a arbitrarily selected people. This is required in all forms of Socialism and it violates the rules of free market (capitalism).
If we look far enough into the past, large enough monopolies are indistinguishable from governments. The Hanseatic League had their own armies, their own laws and even their own cities. Under their rule they fully controlled supply and demand, including price, which no longer makes it a free-market system. Still, they aren't what we define as a state (definitions...).
Taxation don't violate a free market. A free market need laws, which in turn require police and military, which in turn need to be paid (which distributes money). If everyone has to have their own police, military and laws, everyone becomes small islands of states. Those states then violate the supply-demand market, and thus you no longer have a free market.
There is no free lunch here. One can try to redefine what a free market is, what socialism is, what a state is, what a authority is, what taxation is, what interferences is, but it will just ends up arguing definitions.
The traditional definition of socialism is that it has public ownership of the means of production (i.e. shared by society as a whole). What you describe wouldn't achieve that, because, even with market regulations that prevent monopolization, means of production would still be privately owned - there'd just be more such private owners. But the basics of private ownership of the means of production - the ability to extract economic rent from them - wouldn't change, and that basic ability is what defines capitalism.
Socialism just dictates that the workers own the product of their work. A free market socialist economy would be one in which employees owned and democratically controlled businesses and in which it was illegal to sell equity in a business (the stock market simply wouldn't exist).
It could be structured as "one employee one vote" or it could be structured so you earned equity and vote over time (perhaps in proportion to your salary). Capital financing in this economy would happen through bank loans (which wouldn't confer any kind of control), crowd sourcing, and through public means.
This economy isn't centrally planned. The government doesn't own the businesses, the employees do. The government doesn't dictate how they operate, the employees do, democratically. You can still start your own business, and when you're the only employee, you call the shots -- it's only when you hire your first employee that you have to start sharing decision making in some way.
It's free market, because there's still a free market for goods and services. Businesses still compete in a competitive market.
It's a really, really interesting idea. When you dig into it, you find all kinds of fascinating and promising potential side effects of a society and economy shaped this way.
For just one example, it would incentivize innovation and the finding of efficiencies even more powerfully than a capitalistic free market -- because the worker making the innovation would ultimately own and control the business benefiting and so would directly benefit. If a worker came up with a innovation that increased efficiency, that worker would then get a voice in whether the increased efficiency was turned into more wages or more free time. That's a huge incentive. Right now, there's no guarantee that any particular employee will benefit directly from their innovations, so many aren't incentivized to really try very hard at their jobs.
There are many other possible effects of a society structured like this. Among them: - People who get more practice at operating democratically and would thus get better at it. - It might discourage growth after a point - because large democracies get unwieldy fast. - It would naturally resist the concentration of wealth and power because the system would more evenly spread the profits of business. - It would encourage businesses to stay in and be more respectful of the communities they operate in because the people who are calling the shots also live in those communities. - Similarly there might be less of a need for regulation around externalities (like the environment) because the folks calling the shots are the ones living in the communities in which the businesses operate and are directly effected by the externalities.
But it's also an idea that's really hard for a lot of people in our current economy and society to wrap their heads around. The idea that "Free Market Capitalism" and "Totalitarian, Centrally Planned Communism" are the only two systems available is really heavily ingrained in most people. And the concept of a business that operates democratically is totally alien to most. We're just so used to hierarchical, authoritarian businesses that it's hard for many people to even imagine it could be another way.