You Do Need power plug adapter while traveling from Martinique to Norfolk Island.

Here is Why You Need An Adapter

The outlet and plug type used in Norfolk Island is I 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

Norfolk Island

In Norfolk Island, outlets of type I are in use.

Type I