The National Assembly passed the motion by 569-8, bringing into effect a bill first approved by the Senate Upper House in June 2009.
Museums in eight French cities, including Paris, Marseille, Lyon and Rouen, all have Maori heads in their collections. These will be removed from storage and returned to New Zealand within the next year, where they will be given either to relatives or the national Te Papa Tongarewa Museum.
It is the first time that a French law has authorised the return of an entire category of exhibits, rather than a specific object.
"You don't build culture by trafficking. You build culture through respect and exchange," France's Culture Minister Frédéric Mitterand told lawmakers.
New Zealand has been demanding the restitution of the heads since the 1980s.
The heads of high-ranking Maoris, decorated with elaborate tattoos as a mark of social status, were traditionally preserved by their tribesmen in the belief that the practice would keep the dead person's spirit alive.
Brought to Europe and the United States by explorers in the 18th and 19th centuries, about 500 such heads were once to be found in US and European collections. Around 300 have so far been returned to New Zealand.