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

Here is Why You Need An Adapter

The outlet and plug type used in Martinique are C, D and E and in Christmas Island is I. This is how they look like.

Christmas Island

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

Type I

Martinique

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

Type C

Type D

Type E