You Do Need power plug adapter while traveling from Pitcairn Islands to New Caledonia.

Here is Why You Need An Adapter

The outlet and plug type used in New Caledonia are C and F and in Pitcairn Islands is I. This is how they look like.

Pitcairn Islands

In Pitcairn Islands, outlets of type I are in use.

Type I

New Caledonia

In New Caledonia, outlets of type C and F are in use.

Type C

Type F