As Stefan pointed out, D.Duarte has Orléans blood through his mother Pss D.Maria Francisca of Orléans-Bragança.
D.Maria Francisca was sister of D.Isabel O-B, who married Henri d'Orléans, Count of Paris (grand-parents of the current Count of Paris).
The Duke of Bragança and his father, D.Duarte Nuno, were always close to the Orléans.