With any POD prior to 1900, this seems simple enough. Historically, before the Europeans arrived, the native Kanak population of New Caledonia was roughly equivalent to that of Hawaii; and indeed, to the native population of the entirety of contemporary New Zealand. The main difference was in the way the natives were treated. The Kanaks were enslaved, and scattered across the Pacific to be employed as forced labourers on French plantations, ranches and public works- "Blackbirded", in vast numbers. Kanak slaves were exported to such places such as Australia, California, Canada, Chile and Fiji (with the inter-Asian slave trade carrying many of them to India, Japan, South Africa, and what is now Malaysia). By the time that the Kanaks were forced onto Native Reserves in the mountains, the cumulative impacts of the disease epidemics and the slave trade had taken their toll on the Kanak population, and their living conditions became virtually impossible.
The Kanaks were moved onto the Reserves after the French government established a prison colony Australia-style, resettling 20,000 convicts to the island between 1864 and 1897, most of whom settled permanently in the country, who were employed to carry out nickel and copper mining. This caused serious resentment among the Kanaks, who revolted in 1878 against the French colonial rule- but by this stage, it was too late. The Kanak revolt was brutally suppressed by the French, who were far better armed. The Kanak leader was decapitated, and his head was put on display as a trophy of war in the Muséum National d'Histoire Naturelle. Even today, the Kanak population has barely recovered from the trauma, and has only surpassed its pre-contact peak population in the past twenty years.
So, for a potential POD, let's look to OTL first. IOTL, the first American whaler (controlled by the fiercely American loyalist whaling and sealing company, Samuel Enderby & Sons) to come into New Caledonia waters was the
Britannia, in November 1793. This ship discovered the island which they themselves named Britannia (for obvious reasons), and which later became known as
Maré Island (in the New Caledonian Loyalty Islands). In 1806, this same ship grounded on the
Elizabeth Reef ,located 160km North of
Lord Howe Island. Whalers operated off New Caledonia during the 19th century. Sandalwood traders were welcome, but as supplies diminished, the traders became increasingly abusive. Tensions developed into hostilities, and in 1849 the crew of the US vessel
Cutter were killed and eaten by the Pouma clan.
American whalers were dominant in the South Pacific until France annexed New Caledonia in the 1840s. Whaling was mostly concentrated around the
Chesterfield Islands , West of New Caledonia, and to a lesser extent, in the waters to the north of New Caledonia Island and the Loyalty Islands. About fifty American whalers (identified by Robert Langsom from their log books) have been recorded in the region (Grande Terre, Loyalty Is., Walpole and Hunter) between 1793 and 1887. The American whaling operations there peaked between 1835 and 1860- immediately prior to the formal possession of New Caledonia by the French, with the American whalers only relocating their operations elsewhere
after the French
began transporting settlers to their new penal colony, in 1860.
So, for a potential POD; WI the Americans assert their own claim first, with the USA whalers establishing permanent colonial settlements and ports on the island, and subsequently taking formal possession of New Caledonia (or even just the Loyalty Islands and Chesterfield Islands, as a starting point) before Napoleon III and Admiral Febvrier-Despointes manage to assert France's claim to the territory (before September 1853)? Would this be a suitable POD to make New Caledonia more populous? IMHO, if you get some local competition for control between the Americans and the French, along with increased settlement as a result, a present day population on a par with that of the island of Timor seems more than reasonable. On the other hand, the OP's challenge; for New Caledonia to have not just a few million residents, but several million residents, seems a bit too much to accomplish plausibly without ASB intervention.