French Declaration of the Rights of Man and of the Citizen expressed freedom of speech at roughly the same time as american Bill of Rights, and used formulation that is more general and does not restrict just the government:
"The free communication of thoughts and of opinions is one of the most precious rights of man: any citizen thus may speak, write, print freely, except to respond to the abuse of this liberty, in the cases determined by the law."
Before the U.S., nobody even thought free speech was possible. England was the closest, but their version of free speech was still subject to government censorship.
It was the writings of the Founding Fathers, and the Bill of Rights in particular, that established the doctrine that is today known as "freedom of speech."