Louis XIII was a king of France for the time at least including the two years where the Doctor was known to have met him: 1626 and 1637. He was most known for his musketeers and his spiky relationship with Cardinal Richelieu and his wife, Queen Anne.
His marriage to Queen Anne was stormy; both parties took lovers. By 1626, when King Louis XIII met the Fifth Doctor, Peri, and Erimem, Queen Anne had only recently ended an affair with the Duke of Buckingham, and Louis's wandering eye fixed itself firmly on Erimem.
Louis XIII appointed Richelieu his chief minister in 1624, despite a personal and professional rivalry with the Cardinal. By 1626, the king's musketeers and the Cardinal's guards were constantly at each other's throats. (AUDIO: The Church and the Crown)