They issued a statement after the pro-independence FLNKS movement restated its position that Matthew and Hunter islands belonged to Vanuatu's heritage.
The three said last November's independence referendum showed a majority of New Caledonians wanted to stay French.
They said they would therefore oppose any attempt to dispossess the country of part of its land and wealth.
FLNKS leader Daniel Goa said unlike the people of Vanuatu, the Kanaks had no cultural links to the two islands.
He said it was more of a case of France wanting to keep its maritime area, being driven by economic interest.
According to a New Caledonian public law professor specialising in territorial issue, the two countries were likely to keep their territorial dispute out of the courts
Geraldine Giraudeau's comments follow a French naval vessel visit to the islands in January which prompted a rebuke from Vanuatu.
She said litigation over Matthew and Hunter would likely be long and costly, and France's ongoing moves to assert sovereignty wouldn't stand up in the international courts.
"I'm sure that the governments will try everything to reach a negotiated settlement before thinking about any other way of resolution," Professor Giraudeau said.
She said a possible settlement could involve allowing local fishers access which has happened in other territorial disputes.