An airport source told AFP news agency that the woman was a resident of France who was in the process of adopting the child, from Haiti.
French authorities were notified but prosecutors decided not to press charges.
"The cloth bag belonged to a woman sitting at the back of the plane. At one point she opened the bag and her neighbour on the other row of seats saw something moving inside. He alerted flight attendants, who then discovered a baby," a passenger named Vincent told French news website Planet.fr (in French).
Air France says it is investigating the incident.
The stories that affect and influence parents all in one place.