Two groups, Ban Asbestos and Greenpeace, lodged a suit with the Paris administrative court on the grounds that procedures at the Alang naval yard are inadequate to allow the asbestos to be removed without endangering the workers.
They claim that Indian legislation is inadequate to protect employees from the effects of asbestos, which can cause a severe form of lung cancer.
They also contest the French state's claim that the Clemenceau, though decommissioned, is a warship and not bound by the Bale convention of 1989 on the international shipment of dangerous waste.
And they challenge the government's case that a relatively small amount of asbestos remains in the ship after decontamination already carried out in France, saying the true figure is more than 100 tonnes.
The Clemenceau, currently moored in the French naval base of Toulon, is to be towed to India "in the next few days", according to defence ministry spokesman Jean-Francois Bureau.
Greenpeace and other rights groups said in a report earlier this month that countries which send ships for scrapping in India and other developing countries in Asia are condoning a system that claims thousands of workers' lives each year,.
But previous attempts to stop the Clemenceau leaving for Alang, the world's biggest shipbreaking yard, have been shot down by the French courts, which have said they have no power to prevent it.
The Clemenceau, which took part in the 1991 Gulf War, was taken out of service when it was superseded by France's new, nuclear-powered aircraft carrier, the Charles de Gaulle.