French personnel were checked for radioactivity after tests
There is no shortage of people who were present at nuclear tests and now suffer from health problems that, it is widely accepted, could have been induced by ionising radiation.
But when it comes to scientifically proving a definite causal link between illness and radioactive contamination, uncertainty is never far away.
For example, the United Nations only accepts that one illness - child thyroid cancer - can be definitely ascribed to the fallout from the Chernobyl nuclear accident.
The only cases in which a link between a nuclear bomb and illness is rarely questioned are those of Japanese civilians in Hiroshima and Nagasaki exposed to more than 100 millisieverts (mSv) of radiation.
Exposure at nuclear test sites was generally much lower.
"At the moment there is no epidemiological study that has shown a rise in the number of cancers in veterans," says Patrick Gourmelon, a scientist at the French Institute of Radioprotection and Nuclear Safety.
"On the other hand - and here there is a total consensus - we know that with nuclear tests, if one does not protect oneself properly against the effects, there is an increasing risk in the long term for a certain number of identified cancers."
The French government's nuclear test compensation bill is an acknowledgement of this heightened risk for 18 types of cancer listed by the UN.
Studies in Japan also show that there could also be a higher incidence of cardio-vascular problems among those exposed to radiation from nuclear weapons, a link that Mr Gourmelon says is "not proved but strongly suspected".
The French government says that during testing it took all the protective measures for military and civilian personnel considered necessary at the time.
Veterans say there was little awareness of health risks at test sites
But the veterans themselves often remember what they say was a casual approach to safety, telling stories of people dressed in light cotton shorts being sent into contaminated areas.
And in the time since the tests, the perception of risk has changed, eventually arriving at an internationally accepted principle of keeping radiation exposure "as low as reasonably achievable".
There was an important shift, experts say, when the issue stopped being seen as one that centred on physics - the level of radiation to which people are exposed - and the much more complex issue of the biological transformation of cells was taken into account.
It is thought that there is generally a linear relationship between the level of exposure and risk - with risk increasing proportionately as exposure rises - but there is much uncertainty about what the affects of low doses might be, since cells could either repair problems or pass them on.
"You can make reasonable arguments that the relationship is approximately linear, but biological mechanisms are complex and still under intense laboratory research," says Malcolm Crick, secretary of the UN scientific committee on the effects of atomic radiation.
"Right now we don't know conclusively if taken together they would imply linear, a higher risk than linear or a lower risk than linear at these low doses."
Understanding of how damaged cells can pass on this damage to future cells is helping to "explain the very significant delays between the moment radiation took place
and the moment that the illness appears," says Abraham Behar, a professor of nuclear medicine and radiobiology in Paris.
But he adds: "It's because this delay can last 30 or 40 years that it is so difficult to recognise the effects in veterans."
Among 1,800 surviving veterans in France who sent in details of their health to the veterans' association there was an unusually high incidence of certain types of cancers and heart problems - especially among those who took part in atmospheric tests. The results were similar to those for British veterans.
Many of the French veterans also said they were sterile or had children with congenital disorders. Local populations living near the test sites have reported the same problems.
Scientists say no such effect was seen in Japan, and that the idea that health problems could be passed between generations is therefore doubtful, but they do not rule it out.
"We think reproductive cells are so sensitive to radiation that they are killed," says Claude Parmentier, a former head of nuclear medicine at the Gustave-Roussy institute who treated people living near nuclear test sites in French Polynesia.
If they were killed there would be no question of damage being passed on.
But he adds: "There could well be small, micro-lesions that grow with time and that can indeed be a threat for the descendants."
It is among the 10,000 or so test-site workers from French Polynesia "that we can clearly see that there are more health problems than among the rest of the population," says Mr Behar.
But many people at these and other test sites around the world would only have been exposed to the sort of levels of radiation that could occur naturally.
"People think of radiation as something special and extremely dangerous but in fact we're all bathed in radiation from natural sources, such as cosmic rays, as well as being exposed to more common artificial sources such as medical X-rays," says Mr Crick.
"An increase in radiation dose that is a fraction of what we get naturally is generally not going to show up in cancer statistics.
"It doesn't mean that there aren't effects, it just means that normally you're not going to be sure there is a real increase."