There are fears that the referendum could reignite old tensions between indigenous Kanak people and whites who have settled on the islands, which are home to a quarter of the world's known nickel supplies, a vital component in electronics manufacturing.
Ringed by dazzling white beaches and turquoise waters, New Caledonia is one of a handful of French island outposts scattered around the globe -- a legacy of the country's 19th-century empire-building -- which retain strategic importance.
The referendum will be a test of the appeal of remaining part of France for such far-flung territories, which are heavily dependent on state handouts but where many feel overlooked by Paris.
Both French Guiana in South America and the Indian Ocean archipelago of Mayotte have been rocked since last year by major protests over living standards and perceived neglect.
Yet few expect New Caledonia, home to 269,000 people, to vote for independence from France, which claimed the archipelago in 1853.
Indigenous people make up less than half of the electorate, and not all of them want to break free from Paris, 18,000 kilometres (11,000 miles) away.
"We have everything we need with France -- schools, hospitals," said Marceline Bolo, a housewife in the Noumea suburbs, describing herself as "proud to be French".
Surveys suggest between 60 and 69 percent will vote against a split in Sunday's vote, the culmination of a two-decade process that has seen powers devolved to local authorities.
Hundreds of separatists turned out for a final rally in Noumea on Tuesday, waving a sea of colourful Kanak flags to a backdrop of local Kaneka music.
Over the noise of the crowd, Roch Wamytan, leader of the separatist UC-FLNKS alliance, urged Kanaks to seek self-determination from "colonist" France, which he said was hanging on to "the last shreds of its empire".
Yet many "no" voters point to the 1.3 billion euros the French state pours into New Caledonia's coffers every year, fearing for the economy if the archipelago was to go it alone.
Others worry that China could use an independent New Caledonia as a vehicle for its growing influence in the Pacific, following major investment in Vanuatu, another territory which broke from France in 1980.
Leap into the unknown?
New Caledonia already runs its own affairs in many areas, although defence, foreign affairs and higher education are still decided by Paris.
"We are already a semi-independent country -- we exercise many powers, so it wouldn't be a leap into the unknown," said Paul Neaouytine, head of the northern province, a separatist stronghold.
Others say this is precisely the reason why New Caledonia does not need to split from France.
"I don't really understand why we're having such a vote," said retired doctor Rene Gagnolet, resolutely opposed to independence, as he sat in Noumea's market.
The referendum will only serve to "whet the appetites of some against us whites", he predicted.
His table-mate and former patient Sosefo Taofifenua, part of a large minority hailing from another French Pacific territory, Wallis and Futuna, was meanwhile torn.
"My heart is voting with the Kanaks, but my head tells me to stay French," the 72-year-old said, still unsure if he will vote on Sunday.
Decades of resentment, not least over the thousands of hectares (acres) of land seized from indigenous people by colonisers, boiled over into deadly clashes in the 1980s.
The violence, which claimed more than 70 lives, led to the 1998 Noumea Accord which paved the way for devolution and efforts to redress the economic balance..
Yet sharp inequalities remain and New Caledonia's former high commissioner Alain Christnacht, who helped draft the 1998 deal, worries the referendum could revive old animosities.
"Kanaks are working as managers, doctors, engineers, airline pilots. Society has moved forward a lot," he said.
"But there is also, among Kanaks, a faint concern that immigration will bring them to just 20 or 10 percent of the population, like the Maoris in New Zealand or Aboriginal Australians," he added.
"A common society is under construction there, but it's a fragile one."
Under the 1998 deal, in the event of a "no" vote two further referendums on independence could still be held before 2022.