When Becky says that Rose is reading a French novel, the novel, quite obviously, is not in French.
Mrs. Crawley says to Becky, when she is playing the piano, "if music be the food of love", clearly referencing The beginning of William Shakespeare's "Twelfth Night, or What You Will".
Suranne Jones (Miss Pinkerton) & Olivia Cooke (Becky Sharp) also worked together on The Secret of Crickley Hall (2012) as Eve Caleigh & Nancy Linnet respectively.