To the best of my knowledge, the only time there was a Grand Dauphin and a Petit Dauphin was during Louis XIV's reign, his elder son being the Grand Dauphin and his grandson Louis Duke of Burgundy being styled the Petit Dauphin and upgraded to just Dauphin after his father's death.

Oddly, Burgundy's son, the future Louis XV was never styled as the Petit Dauphin, just the Dauphin at his father's death.

Louis XV himself was not succeeded by a son but by his grandson Louis XVI.
Again Louis (XVI) was not styled Petit Dauphin during his father's life, just Dauphin after his death, so I guess there was just one occasion when that style was used.