When it can remain part of a prosperous French Republic, why would it want to leave? The economy would be far more unstable without the guarantee of French support, and this could damage the morale of a newly created nation.
What's more, an independent country means free choice of ideology. Although it's almost certain New Caledonia would retain their current ideology, they could start another global conflict of ideologies - however, this is the risk with any independent country.
All in all, the New Caledonian territory would benefit France's economy in the same way France's backing would keep the island territory stable. There is no outstanding reason for them to gain independence from France.