Petit-Fils de France
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Petit-Fils de France, meaning "Grandson of France", was the title given to the sons of Fils de France who were themselves the sons of the kings and dauphins of France. Their daughters would have the title Petit-Fille de France which means "Granddaughter of France."
Thus, a Petit Fils de France was usually a grandson of a French king or of a dauphin. The principal exception was that the children of a dauphin (being the eldest son and heir) were given the same status as if they were the king's children instead of his grandchildren.
A king could, if he were so inclined, permit persons who were not actually his grandchildren to use the titles Petit-Fils or Petit-Fille. In any case, those entitled Petit-Fils or Petit-Fille used the style of Royal Highness.