It was time to investigate health complaints reported by staff who took part in tests, Defence Minister Herve Morin said.
Mr Morin told Le Figaro France should be "true to its conscience".
France carried out more than 200 tests, firstly in Algeria and later in French Polynesia, between 1966 and 1996.
Mr Morin said about 150,000 civil and military workers were "theoretically affected" by the tests.
Mr Morin said an independent commission would examine claims on a case-by-case basis.
He added that 10m euros ($13.6m; £9.3m) had already been earmarked to compensate victims.
France had previously refused to officially recognise a link between its nuclear testing and health complaints reported by both military and civilian staff involved in the tests.
"(French) governments believed for a long time that opening the door to compensation would pose a threat to the very significant efforts made by France to have credible nuclear deterrent," said Mr Morin.
"But it is time for France to be true to its conscience."