The French joint law commission has decided to remove the term negligible risk from the nuclear compensation law in what is seen as a breakthrough for French Polynesia's test victims.
The unanimous decision is now to go to the National Assembly and the Senate for approval as Paris is to make good on its promise to loosen the law.
The compensation law, drawn up by Herve Morin when he was the defence minister in 2009, has been widely criticised for being too restrictive because almost all claims have been thrown out.
A month ago, two French lawmakers urged the social affairs minister Marisol Touraine to amend the decree on compensation to ensure that unsuccessful claimants can resubmit their files.
One of the MPs Jean-Patrick Gille said veterans would find it incomprehensible if the earlier rejection of their compensation bids were to be final.
France tested its atomic weapons first in Algeria and then from 1966 to 1996 in the South Pacific in a programme which involved more than 100,000 personnel.