Oscar the Parrot might be the one I saw. He was a childparrot then. He was in care of the woman in question.
The program was not a serie, so no luck on that one.
Another memory form the program was about a racehorce, that was very ill. The (lovely) woman was called and talked with the horse to find out what was wrong. She said the horse said that it was exhausted from to much and hard traning. She orderd the horse to have some rest and went off. Weeks later she came back and and saw that the state of the horse had not betterd. The trainers swore that they had giving the horse plenty of rest. She talked again with the horse and it said it had been trining as has hard as usual and had not have any rest. The woman confronted the trainers with this information and they had to admit that they had not been giving the rest.
The reason I came to think about the woman was because I saw the 1972 movie Brother Sun, Sister Moon about the saint Francesco, with a friend. We spoke about what stories had been omitted from the movie. And one of the stories omitted is about Francesco talking with the animals.
He was in doubt about that story and I rememberd the woman from the program.