The Ballet Teacher is a Springfield Elementary School employee, who teaches the school ballet class. She speaks with a French accent, showing that she's originally from France. Since the ballet teacher is apparently French, it could be a reference to how ballet became further developed in France after it originated in Italy during the Italian Renaissance.
In Homer vs. Patty and Selma, Bart forgets that it's P.E. sign-up day at school and is forced to sign up for ballet, as all the other sports were full and the ballet class was the only one that had any open spots. At first, Bart was embarrassed about being the only boy in the class, but he eventually started to enjoy ballet and found that he was actually pretty good at it.