Factual error: The schoolmaster chastises Belle for teaching a little girl to read. But in 1692, a time before the story is set, King Louis XIV issued a royal decree requiring villages to establish schools and requiring all parents to send their children - boys and girls - to the village schools until they were 13 years old.
Factual error: The head master of the school criticizes Belle for "teaching another girl to read." But beginning in 1692, well before the movie is set, all parents in France were required, by royal decree, to send all their children, boys and girls, to school until at least age 13.
Answer: She didn't have to, the second Belle proclaimed her love for the Beast, the spell was broken. She would have seen her use her magic to reverse the curse. It would be obvious to everyone she was an enchanted being.