Two groups, Ban Asbestos and the National Association for the Defense of Asbestos Victims, or ANDEVA, had talks Friday with the office of France's defense minister, Michele Alliot-Marie.
"We disagreed (on the issue) and due to that we will pursue legal action," said Annie Thebaud-Mony, a spokeswoman for Ban Asbestos.
The dispute centers on the amount of asbestos still present in the ship, "between 140 to 180 tonnes", Thebaud-Mony said.
According to the government, 115 tonnes of the ship's asbestos-laden insulation have already been removed in the French southern port city of Toulon and there are only several dozen tonnes of asbestos left.
The Clemenceau will leave for a shipbuilder in India "in the next few days", said ministry spokesman Jean-Francois Bureau, who added that in order to tow the mothballed ship to India it could not be totally dismantled in France.
Greenpeace and other rights groups have argued against the industrialized nations exporting ships to Asia where the workers in the shipyards are not sufficiently protected from dangerous substances such as asbestos.