You Do Need power plug adapter while traveling from Martinique to Cook Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cook Islands 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

Cook Islands

In Cook Islands, outlets of type I are in use.

Type I