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

Here is Why You Need An Adapter

The outlet and plug type used in Falkland Islands is G and in New Caledonia are C and F. This is how they look like.

New Caledonia

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

Type C

Type F

Falkland Islands

In Falkland Islands, outlets of type G are in use.

Type G