Veterans and workers who fell ill after France's nuclear tests in Algeria and the South Pacific said the government's measures to compensate victims did not go far enough.
Defence Minister Herve Morin visited the headquarters of a new committee set up to evaluate claims by victims of the 1960-1996 tests, saying he hoped the government's gesture would help "our country be at peace with itself".
But victims' associations said the government ruled out compensating many people who should qualify.
Some 150,000 people, including civilian and military personnel, were on site for the 210 tests France carried out, both in the atmosphere and underground, in the Sahara Desert and the South Pacific.
Based on a law passed last year, compensation is to be decided on a case-by-case basis. Victims submit their claims to the committee Mr Morin visited in the Paris suburb of Arcueil. The committee, just starting its work, said it has received about 20 claims so far.
Depending on the severity of victims' ailments, those who are approved by the committee will likely receive compensation in the realm of 50,000 to 90,000 euro, the Defence Ministry said.
The Association of Veterans of Nuclear Tests, known as Aven, and Moruroa e tatou, an association of Polynesian workers sickened by radiation, complained that the government does not recognise enough cancers in its list of ailments that qualify for compensation.
In a joint statement, they said male breast cancer and more types of thyroid cancer should be included on the list. The defence minister said the list of ailments "takes into account the most recent scientific reports".
The victims' associations also said the geographical restrictions are too narrow.
"While all of Polynesia was greatly contaminated by the 41 atmospheric tests between 1966 and 1974, Morin's decree said radioactive clouds fell selectively on only four islands or atolls and on a few communities in Tahiti," the statement said. Mr Morin retorted that the geographic limits "correspond to the zones in which there was significant fallout."