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

Here is Why You Need An Adapter

The outlet and plug type used in Nauru 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

Nauru

In Nauru, outlets of type I are in use.

Type I