Eldest son of a French king (7)
I believe the answer is:
dauphin
'eldest son of a french king' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for dauphin that I've seen before include "King of France's heir" , "former royal" , "Heir apparent to the French throne" , "Formerly, the eldest son of the King of France" , "French royal heir" .)