You Do Need power plug adapter while traveling from Martinique 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 Martinique are C, D and E. This is how they look like.

Martinique

In Martinique, outlets of type C, D and E are in use.

Type C

Type D

Type E

New Caledonia

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

Type C

Type F