"Free market" is a political buzz phrase with no real meaning in economics (look it up).
While I agree that "free market" is mainly a political term... in economics the same concept is simply referred to as a "market". There is no need for a term like "free market" in economics because in economics all trade is assumed to be voluntary, and consequently all markets are free markets. Occasionally economists will speculate on the likely effects of non-economic influences like price floors or taxation, but the very existence of these influences undermines the most basic foundations of economic calculation. This is part of the reason why economic predictions tend to go off the rails when you start introducing distortions like patents, copyrights, monetary policy, and taxes, all of which are decidedly non-free: they belong to the domain of political action rather than economics.
There is also no such thing as a free market when there is no regulation...
That is the same as saying "there is no such thing as a free market." A regulated market cannot by definition be a free market. The "free" in "free market" means that all interactions within the market are voluntary: the permissible actions are exactly those which do not infringe on others' property rights, no more and no less. Regulations are imposed involuntarily. The two are not compatible.
A free market may well include monopolies and cartels, but in general these are due to the presence of regulations, not their absence. The more heavily regulated the market the higher the barriers to entry and the more prone it becomes to regulatory capture, both of which favor a small number of large, well-established players.