An initial sum of €10 million ($14 million) has been set aside for military and civilian staff as well as local populations who fell ill from radiation exposure, Defence Minister Herve Morin said.
Some 150,000 civilian and military personnel took part in the 210 nuclear tests carried out in the Algerian Sahara desert and the Pacific between 1960 and 1996.
"It’s time for France to be true to its conscience," Morin told Le Figaro newspaper.
The move was welcomed by French veterans who had been waging a long campaign for the state to recognise its responsibility toward ageing and sick staff of its nuclear programme.
"This is a step forward that we are greeting with satisfaction," Michel Leger, president of the Association of Veterans of Nuclear Tests, told AFP.
Leger recalled he was "wearing shorts and a hat, lying on the ground without protective eyewear, arms folded over my eyes" when an above-ground test took place 40 kilometres (25 miles) away, in southern Algeria in the early 1960s.
"Afterwards, there was no medical checkup," said Leger, who now suffers from cardiovascular illnesses.
One of the world’s five declared nuclear powers, France carried out 17 nuclear tests in Algeria in the early 1960s including four atmospheric trials, AFP reported.