The ruling is in line with last month's expert advice, which took into account a law change that reintroduced a minimum figure of radiation exposure.
Earlier this year, the expert advice was to compensate the claimants.
The law change was inserted into the Finance Act in December reportedly to comply with the Public Health Act.
The veterans groups have been dismayed at the law change, saying now no more applications are likely to succeed.
The French Polynesian government has, however, defended the law change and urged opponents to accept the new compensation regime.