You Do Need power plug adapter while traveling from Nauru 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 Nauru is I. This is how they look like.

Nauru

In Nauru, 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