Actually with New Orleans it was because the ordinance was overly broad that prohibited such language. Essentially, it made it so that whether or not they were, in fact, words that could be construed as "fighting words" became "immaterial", as the
only thing under consideration in the case was the wording of the ordinance, not the wording of the attack.
It clearly states that in the decision of
Lewis v. New Orleans.
It wasn't actually a "fighting words" decision, it was a decision that stated the ordinance in question did not
limit itself to fighting words.
That's why the plaintiff won the case. Not because the words she used were not considered fighting words. Actually, they
were pretty much considered fighting words by the court. That was just immaterial to the decision.