Louis Alphonse, Duke of Anjou
Their father has conferred upon them the historic French titles of, respectively, Duke of Burgundy ("duc de Bourgogne"), and Duke of Berry ("duc de Berry"). (In Spain, the twins are "Don" Luis and "Don" Alfonso de Borbón Vargas). Prince Louis, as Legitimist Dauphin of France, is expected to succeed his father as head of the French royal house, the senior Bourbon/Capetian line, in Legitimist reckoning. However, under Spanish law, and assuming Felipe VI does not in future father a son, the Spanish crown will be inherited by his elder daughter Leonor, Princess of Asturias, who will become queen regnant, and if Felipe does have a son, that son will inherit the Spanish throne regardless of the genealogical seniority of the Anjou branch. Louis and Alphonse were baptised on 5 September 2010 at St Peter's Basilica in Vatican City. Louis' godparents were Arancha Martínez-Bordíu and Francisco D'Agostino and Alphonse's were Amparo Corell de Trenor, and Lorenzo Perales.
Prince Jean, Duke of Vendôme
The couple have five children: He was created Duke of Vendôme (French: "Duc de Vendôme") by his paternal grandfather, on 27 September 1987. 
Jean is a member of the House of Orléans, a cadet branch of the House of Bourbon, itself a cadet branch of the Capetian dynasty. His patrilineal ancestors, or direct male-line ancestors, include many of the Kings of France.