As I interpret it, a mask is what you wear on your face and a masque is a costume party or event at which people are in masks, for example Edgar Allan Poe’s story “The Masque of the Red Death.”
1: a form of amateur dramatic entertainment, popular among the nobility in 16th- and 17th-century England, which consisted of dancing and acting performed by masked players.
2: variant spelling of mask ( sense 1 of the noun).
I would not use them synonymously.
“I wore my mask while attending the masque.”: (masquerade or masked ball.