First let's setup some terminology so we're not confusing terms.

Free means no money, or monetary value, is needed. i.e As in "free beer"

Free can also mean no obligations or reprehensions, e.g. Free speech.

To avoid confusion let's refer to the freedom one as Libre, i.e. free beer, libre speech.

Secondly I never said communism, since communism has a hard definition imposed by their creators, I said left-wing, for the purposes of this discussion let's agree on a middle term of socialism to mean the opposite of capitalism, or if you prefer a type of government associated with left wing parties, which involve social policies and free services.

With those definitions out of the way: Is any free society by definition socialist? It is my opinion that yes, any society that's past the need for money it's by definition socialist, whereas any society that uses money (or monetary equivalents) it's capitalist.

Libre or authoritarian governments can exist on either side of the spectrum of economical policies, so if you meant to ask whether is any libre society by definition socialist? My answer would be no, you can have societies where you have freedom but things cost money. That being said I believe that no society can be truly Libre unless the basic structure and needs are free.