The central conflict of this story is twofold, how? Let me explain it you.
Beauty lives with Beast to save her family and fulfill father’s promise, and confronts fear that she could never go back to her family again and has to adapt herself with Beast. On the other hand, Beast also confronts his demon inside, falls for Beauty and needs to prove his feelings of love for her, thus wishes her to stay with him. Beauty starts her journey from father’s house to castle and saves her family, however ultimately saves Beast too.