Lawmakers in Paris voted 351 to 153 in favour of the bill to allow French residents who have lived in New Caledonia for 10 years to vote in provincial elections - a move local leaders fear will dilute the indigenous Kanak vote.
The French government says the change is needed so elections are democratic in the country's territory.
On Wednesday morning, Lilou Garrido Navarro Kherachi, 19, drove around protester blockades in Noumea and saw burning cars and buildings, including a ruined veterinary clinic where the neighbours had evacuated the animals before the fire spread.
Police were outnumbered by protesters, she told Reuters.
"The real problem is the youngsters who trash, burn and loot. We didn't see any police deployed on site," she said.
French retailer Decathlon said in a statement its New Caledonia store had been vandalised, looted and burnt overnight, after 10 years of trading.
The New Caledonia government in a statement schools would stay closed, after some were damaged.
French President Emmanuel Macron condemned the violence and called for calm in a letter addressed to officials in New Caledonia that was published on the Facebook account of one lawmaker. The major pro-independence political group, FLNKS, also issued a statement on Wednesday calling for calm and condemned the violence..
Most residents were staying indoors. With stores closed breastfeeding mothers were organising to share milk with mothers who have none left to feed their babies.
