A judge at the Paris administrative court ruled that the campaigners had raised "no serious doubts" about the legality of the aircraft-carrier Clemenceau's transfer to India, where it is to be broken into scrap.
French authorities were waiting for the legal green light to tow the Clemenceau, currently docked at the French naval base of Toulon, to Alang in north-western India, home to the world's biggest ship-breaking yard.
Environmentalist group Greenpeace and three anti-asbestos groups have tried for months to block the move, on the grounds that Indian shipyard workers are not properly protected from the hazards of working with asbestos.
Representing the state, lawyer Joel Alquezar argued in court that the groups were wrongly creating "the impression that India is a lawless state".
The groups also argued that the French state's decision to export the mothballed ship violates rules on the handling of dangerous waste.
But Paris argues that the Clemenceau, although decommissioned, is a warship and so not bound by the Bale convention of 1989 on the international shipment of dangerous waste.
The Clemenceau, which took part in the 1991 Gulf War, was taken out of service when it was superseded by France's new, nuclear-powered aircraft carrier, the Charles de Gaulle.
Marine authorities in Toulon said on Thursday the Clemenceau was ready to leave as soon as it was authorised to do so.