The French defence minister, Herve Morin, has presented to cabinet his nuclear victims' compensation law which could come into effect before the end of the year.
The law marks the first time Paris accepts a link between its more than 200 weapons tests in Africa and the South Pacific and the illnesses of those exposed to radiation.
According to the AFP news agency, the first compensation payments could be made next year.
14 million US dollars has been set aside for compensation payments.
Apart from civilian populations, about 150,000 French and local military personnel were exposed to the French nuclear weapons testing regime.
Mr Morin has said he thinks there were several hundred people who could have suffered from the tests.