"The woman is speaking."
Translation:La femme parle.
No, they are different words, although the meanings are similar. "Parler" means "to speak" (which is what's being asked for here), while "dire" means "to say."
The way I've heard it explained (and I hope one of the experts will correct me if I'm wrong!) is that "parler" is used when you're talking about speaking in general "She is speaking at the conference" or "I am speaking now". "Dire" is when you're relaying specifically what someone actually says: "I am saying yes" or "She says that she is here."
I hope this helps!