Why do you think that Frank chooses not to tell his grandparents that he is living in Montpellier?

Frank does not want his grandparents to find out that he has a criminal background. He never knows when the police might catch up with him. It would also be very hard for him to explain to his grandparents why he is not using his own name, Frank Abegnale, but instead, is living under the name Robert Monjo. He may also feel that he loses his grandparents' respect if they realize he is simply loafing and not pursuing his education at all.