A free market is, by definition, a market which is not regulated at all. A truly free market only exists in anarcho capitalism. Any state-imposed regulation which affects businesses means that a market is not 100% free anymore.
When you have a 100% unregulated market, then monopolies can occur under certain conditions. That's usually the case when you have a fungible product which also gets cheaper to produce the more you produce of it. When the product is fungible, companies can only compete by price, which means small competitors have no way to compete with larger ones, which means only the largest competitor can prevail.
Common regulations to prevent such monopolies are:
- Anti-trust regulations which forbid large companies from cooperating with each other to prevent price-fixing or the largest companies from fusing into one which can then dominate the market. However, this doesn't always work because market leaders can also emerge naturally through destructive competition and price-fixing can be hard to prove.
- Setting minimum prices to ensure that the small companies still have a profit margin which allows them to survive.
- Force companies to sell permission to use their infrastructure to competitors at fair prices (example: a law which says that a train company must sell their competitors licenses to use their rails and train stations).
But any form of regulation means that your economy is less of a free market economy and more of a social market economy. Note that a social market economy is still different from a socialist economy. In a socialist economy, the government controls companies directly, not indirectly through laws and regulations, which means that the state becomes the monopolist and there is no market anymore.