The French defence ministry is reported to have made some changes to the nuclear victims' compensation law due to be approved by the government ahead of its presentation to parliament.
The law marks the first time Paris accepts a link between its more than 200 weapons tests and the illnesses of those exposed to radiation.
According to the AFP news agency, the changes include the extension of the coverage zone to Hao Atoll as well as Taravao in French Polynesia.
The report also says the ministry no longer opposes the creation of a committee that includes veterans' associations keen to follow the plan's implementation.
But the ministry continues to object to set up a compensation fund akin to the one in place for those whose health suffered because of exposure to asbestos.
Apart from civilian populations, about 150,000 French and local military personnel were exposed to the French nuclear weapons testing regime.
In March, the French defence minister, Herve Morin, said he thought there were several hundred people could have suffered from the tests.