The majority of the state news agency says New Caledonia's Congress members have spoken out in favour of changing the electoral law after four government collapses this year.
The proposal by Paris, which it plans to pass within weeks, is to give a government an 18-month grace period before it can be brought down.
Under the current provisions, a single minister's resignation triggers the government's fall and prompts an election in the Congress within two weeks.
Following consultations in Noumea, 31 of the 57 Congress members have expressed their conditional support for the reform plan.
From the end this week, all party leaders will be in Paris to meet the French prime minister, Francois Fillon, for further discussions on the territory's future as it approaches the final phase of the Noumea Accord which provides for a possible referendum on independence.