Its leaders affirm that for nearly 170 years, France and New Caledonia have shared the same path and now share an identity nourished by a language.
The UDI included three of the four members of the French legislature in New Caledonia who were all opposed to independence.
Last week, two right-wing parties in France also spoke out against the choice of New Caledonia for independence.
In the first of three possible referendums two years ago, nearly 57% voted for the status quo.
New Caledonia has been on the UN decolonization list since 1986.