Around 150,000 civilian and military personnel took part in 210 nuclear tests carried out by France between 1960 and 1996.
The upper house Senate is expected to follow suit next Tuesday, scrapping barriers to compensation that deemed most claimants to have been at "insignificant risk" of developing a radiation-induced illness.
Around 150,000 civilian and military personnel took part in 210 nuclear tests carried out by France between 1960 and 1996 in the Pacific and the Sahara desert. Thousands of them later developed serious health problems.
Only around 20 of approximately 1,000 people who filed complaints against France have received compensation.
Ahead of Thursday's vote, Tahitian MP Maina Sage said extending compensation to other sufferers would "finally appease somewhat (the) deep trauma" caused by a "state (that) operated with full awareness of the consequences".
The Mururoa and Fangataufa atolls saw 193 nuclear tests over three decades until then-president Jacques Chirac called a halt to the programme in the 1990s.
France long denied its responsibility for the health and environmental impacts out of fear the admission would weaken its nuclear programme during the Cold War.
It was only in 2010 that France passed a law authorising compensation for military veterans and civilians whose cancer could be attributed to the test programme.
During a visit to French Polynesia in February 2016, President Francois Hollande acknowledged the deleterious effects on health and the environment and pledged to revamp the compensation process.
Hollande also said France would provide financial assistance to the oncology department of Tahiti's hospital, in line with demands from local politicians.
Starting this year, France will pay more than 90 million euros ($96 million) a year to boost the facilities.
It was above the Fangataufa atoll that France launched its first H-bomb in August 1968.
French Polynesia, with a population of about 280,000, is one of three French territories in the Pacific.