The Dauphin of France (French: Dauphin de France, IPA: [dofɛ̃])—strictly The Dauphin of Viennois (Dauphin de Viennois)—was the title given to the heir apparent to the throne of France from 1350 to 1791 and 1824 to 1830. The word is French for dolphin, as a reference to the depiction of the animal on their coat of arms.
The first French prince called le Dauphin was Charles the Wise, later to become Charles V of France. The title was roughly equivalent to the English (thence British) Prince of Wales, the Scottish Duke of Rothesay, the Portuguese Duke of Braganza, and the Spanish Prince of Asturias. The official style of a Dauphin of France, prior to 1461, was par la grâce de Dieu, dauphin de Viennois, comte de Valentinois et de Diois ("By the Grace of God, Dauphin of Viennois, Count of Valentinois and of Diois"). A Dauphin of France united the coat of arms of the Dauphiné, which featured Dolphins, with the French fleurs-de-lys, and might, where appropriate, further unite that with other arms (e.g. Francis, son of Francis I, was ruling Duke of Brittany, so united the arms of that province with the typical arms of a Dauphin; Francis II, while Dauphin, was also King of Scots by marriage to Mary I, and added the arms of the Kingdom of Scotland to those of the Dauphin).
More information, and a list of Dauphins, on the Wikipedia page 
See also Dauphin of Auvergne