The child was fatally injured from hot water burns, the regional prosecutor from Saint-Etienne said.
Her twin brother, who was sharing the bath, suffered burns to one foot, the prosecutor said.
Medical attendants responding to a call from the parents were unable to save the baby girl who died on the spot.
The boy was transported to a hospital in Saint-Etienne.
The incident probably resulted from a faulty manipulation of the hot water tap by the toddlers, according to information from the prosecution and emergency officials called to the scene.
The health of the girl who died had been particularly fragile since her birth, the prosecutor said.
An investigation into the case continues.