Earlier quoted context omitted.
That term is an oxymoron.
This will just end up being a discussion about definitions, but lets dip into it. 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 Ma…
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.