A gentleman offers his arm to a lady, he does not take liberties, even with a hovering hand.
Address the princesses as "your highness" (or, if a queen, "your majesty"). After that you can say, "ma'am", but being a commoner, you'll eat your vowels and pronounce it as 'mum'.
It would be a kindness to ask a polite question regarding the royal's known exploits, e.g., "You highness, what was the most interesting thing about moving into a royal palace?" (applicable to Belle, Ariel, and Cinderella).
When you first enter, a royal will greet you with a photopass photographer at the ready. "C'est Belle! Magnifique!"
As they come to the table, you'll have to take your own pictures. So, have your cameras ready.