Greenpeace lawyer Alexandre Faro said the case was about a "fraudulent invasion of privacy".
The group suspects Areva used an investigative service to hack into its computers to gain secret or private information.
French Sunday paper Journal du Dimanche recently wrote that Geneva-based investigative firm Alp Services had written a "confidential" report in March last year on Greenpeace, corruption watchdog Transparency International and environmental research group Worldwatch.
Six months later Alp Services wrote another report on Areva's former chief executive Anne Lauvergeon and her husband, energy consultant Olivier Fric, according to media reports.
Lauvergeon and her husband last week filed suit for violation of professional secret, breach of trust and misappropriation of funds, they said.
A spokesman for the Areva group said on Tuesday that "there was never any order from Areva to investigate the non-governmental organisations".