You Do Need power plug adapter while traveling from Chile 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 Chile are C and L. This is how they look like.

Chile

In Chile, outlets of type C and L are in use.

Type C

Type L

New Caledonia

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

Type C

Type F