Louis Cunningham, who portrays Louis XVI and grandson of Louis XV, is in real life indeed a direct descendant of Louis XV,, who is his grandfather eight times over.
The portrait Marie Antoinette sends to her mother is actually a depiction of Yolande painted by Elisabeth Vigée-Lebrun in 1782.
James Purefoy who plays Louis XV had previously played royalty. In the movie The Knights Tale he played Edward of Woodstock, The Black Prince who was the son of King Edward III of England.