The Fairness Doctrine required broadcasters to express particular sides and opinions of arguments. This sounds good in theory, but imagine if it were used by creationists who say their "side" of how life came to be, despite being factually wrong, they'd get "fair time" on a subject they don't deserve time on.
No, the Fairness Doctrine wouldn't uphold Free Speech in First Amendment. In my opinion, there would be another way to obtain the true free speech in the first amendment. Free Speech is subjective, so Fairness Doctrine would not be enough to emphasize the free speech in the First Amendment in this case.