The Oxford Dictionary definitions provide a good starting point, and align well with how economists generally use these terms. However, as various comments have noted, formal definitions will differ. This will especially be true for "free market", because it is not a technical term in economics.
Perfect Competition: The situation prevailing in a market in which buyers and sellers are so numerous and well informed that all elements of monopoly are absent and the market price of a commodity is beyond the control of individual buyers and sellers.
Free Market: An economic system in which prices are determined by unrestricted competition between privately owned businesses.
For perfect competition, the key feature is that the market price is beyond the control of individual buyers and sellers. The way this is often formally stated is that the elasticity of demand is zero for every individual seller, and the elasticity of supply is zero for every individual buyer.
For the free market definition, the key point is that interactions are unrestricted. That means, for example, no government intervention. Wikipedia and a few other sources suggest that free markets preclude market power. If you take that view, then a free market implies perfect competition since no market power means zero elasticities.
However, most definitions of a free market do not rule our market power. In that case, the presence of any of a host of imperfections (e.g., imperfect information, barriers to entry) can generate market power, and therefore imperfect competition despite interactions being unregulated. The distinction then seems to be the lack of external intervention.