Charles, Prince Napoleon, and his ex-wife Princess Beatrice of the Two Sicilies are 5th cousins through King Ferdinando I of the Two Sicilies.
Ferdinando I of the Two Sicilies - Maria Amelia of Naples and Sicily - Louise d’Orleans - Leopold II of the Belgians - Clementine of Belgium - Louis, Prince Napoleon - Charles, Prince Napoleon
Ferdinando I of the Two Sicilies - Francesco I of the Two Sicilies - Ferdinando II of the Two Sicilies - Alfonso of the Two Sicilies, Count of Caserta - Ranieri of the Two Sicilies, Duke of Castro - Ferdinand of the Two Sicilies, Duke of Castro - Princess Beatrice of the Two Sicilies
The former spouses are also 5th cousins once removed, again through King Ferdinando I.
Ferdinando I of the Two Sicilies - Luisa of Naples and Sicily - Maria Theresia of Austria, Princess of Tuscany - Vittorio Emanuele II of Italy - Clothilde of Savoy - Victor, Prince Napoleon - Louis, Prince Napoleon - Charles, Prince Napoleon
Ferdinando I of the Two Sicilies - Francesco I of the Two Sicilies - Ferdinando II of the Two Sicilies - Alfonso of the Two Sicilies, Count of Caserta - Ranieri of the Two Sicilies, Duke of Castro - Ferdinand of the Two Sicilies, Duke of Castro - Princess Beatrice of the Two Sicilies