The French Senate has voted in favour of a revision of French Polynesia's autonomy statute.
The reform is contained in two laws which are expected to be adopted in a final reading next week.
The new statute gives official recognition to French Polynesia's contribution to France developing its nuclear deterrent.
It states that consequences of the tests have to be taken into account in every sphere.
France's Overseas Territories minister Annick Girardin said this recognition was a response to the expectations of French Polynesia's people and government.
French Polynesia's president Edouard Fritch is in Paris for the senate sitting.
Ahead of it he said the main point in revising the statute was to calm domestic and international opinion about the legacy of the French nuclear weapons tests.
He said the nuclear issue was also being talked about a lot at the United Nations which six years ago returned French Polynesia onto the decolonisation list.
France carried out 193 nuclear weapon tests in the South Pacific between 1966 and 1996.