Emergency services vehicles were called to the scene, but the woman was later pronounced dead.
A second woman, aged 20, was taken to hospital after also being badly injured in the incident on Monday night.
Marc Petit, mayor of Firminy, said she was in a critical condition on Tuesday, according to the regional newspaper.
Witnesses say there were strong winds on Monday which may have affected the ride at the at the Vogue des Noix funfair.
Local media report the seat in which the two women were sitting hit another carousel nearby. However, this has not been confirmed.
An investigation has been launched into the cause.
Four people, including the owners and operators of the affected rides, were taken into police custody following the incident, according to Le Progres.
Mr Petit is expected to speak at a meeting at the town hall in Firminy on Tuesday.
Last week, a woman was left with serious injuries after being flung from a ride at a fair in Hull.
It is believed she fell from the spinning Airmaxx360 attraction onto the base of a nearby ride, hitting a teenage boy on the ground in the process.
The boy escaped with minor injuries.
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies