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

Here is Why You Need An Adapter

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

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

Type C

Type F

In New Zealand, outlets of type I are in use.

Type I

I am from

going to