You Do Need power plug adapter while traveling from Costa Rica 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 Costa Rica are A and B. This is how they look like.

Costa Rica

In Costa Rica, outlets of type A and B are in use.

Type A

Type B

New Caledonia

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

Type C

Type F