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

Liechtenstein

In Liechtenstein, outlets of type C and J are in use.

Type C

Type J

New Caledonia

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

Type C

Type F