Lawyers acting for the French state say the illnesses claimed by four French Polynesian nuclear test veterans in a Tahiti court were not the result of exposure to radiation.
The case in the Papeete Labour Court concerns four people whose lawyer accused the French Atomic Energy Commission and the military of failing to protect their health.
Two of the veterans have died since filing their complaint.
One of the complainants says after working on the test sites for 25 years he got cancer and lodged a compensation demand.
He says for 11 years he has had no response.
A ruling is expected in mid-July.
More cases are due in court this week.
Two years ago, the then defence minister, Herve Morin, pushed through the compensation law which for the first time acknowledged that the French weapons tests were not clean, but critics say the law is too restrictive.