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

Here is Why You Need An Adapter

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

Saint Barthélemy

In Saint Barthélemy, outlets of type C and E are in use.

Type C

Type E

Martinique

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

Type C

Type D

Type E