In ancient Athens they spoke (ancient) Greek, so no they didn't have an ideal of "free speech", as in the modern US, they had ideals of isegoria and parrhesia - separate concepts that Athenians at least recognised were often irreconcilably in conflict with another. Any such nuance is completely lost in most modern applications.
I think it unlikely that Ancient Athens was heavily influenced by US culture on the topic of free speech as an ideal: https://www.britannica.com/biography/Socrates/The-Athenian-i...