French Polynesia's pro-independence opposition claims France was aware its nuclear weapons tests were harmful while professing that they were clean.
The Tavini Huiraatira Party said this amounted to a crime against humanity which it wants to take to the UN Human Rights Commission in Geneva.
A Tavini assembly member Richard Tuheiava said to take France to the ICC, French Polynesia would have to be an independent country.
"So that is why we are trying to start up our process by raising this case before the human rights committee in Geneva, which is the committee which we can legally stand before," Mr Tuheiava said.
He said his party was building momentum with a petition being circulated in the territory.
France, which carried out 193 tests in the South Pacific, is amending its compensation law for test victims after many found it to be inadequate.