A map unearthed by the Le Parisien newspaper shows fallout from the test of the Gerboise Bleue bomb in the Algerian desert reaching western Sicily and southern Spain on the 13th day after the test.
In related documents, declassified last year due to a legal case brought by veterans of France's nuclear tests, the military claims that doses were low but expert Bruno Barillot tells Le Parisien that "the norms at the time were a lot less strict than today".
The documents also admit that dangerous levels of iodine-131 and caesium-137 were found in Chad's capital, N'Djamena, as well as Arak, near Tamanrasset in southern Algeria.
"Everybody knows today that these radioactive elements cause cancers or cardio-vascular diseases," Barillot said.
"This means tens of thousands of potential victims," lawyer Fatima Benbraham, who is representing about 30 cases in Algeria, commented.
"None have received compensation because we don’t have proof that they were in the very limited zone laid down by the law relating to damages," Barillot told RFI.
The map shows that Algeria and practically the whole Saharan region was contaminated following the tests, he says.
"So we think that the French government must review its law and enlarge the zones concerning Algeria. For the tests carried out in French Polynesia for example [1959 to 1996] in December 2013 we managed to get the law on compensation modified so that the geographical zone in which people can get compensation be extended to cover all of Polynesia . Now France must do the same for Algeria."
Gerboise Bleue (blue jerboa) was the first nuclear bomb tested by France.
It was four times as powerful as the bomb dropped by the US on Hiroshima.
France carried out 210 nuclear tests in Algeria and Polynesia between 1960 and 1996.
Veterans who were present during the tests have suffered cancer and other diseases and have been fighting for compensation for years but only a small number of cases have been accepted as valid.