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

Here is Why You Need An Adapter

The outlet and plug type used in Saint Barthélemy are C and E and in Cape Verde are C and F. This is how they look like.

Cape Verde

In Cape Verde, outlets of type C and F are in use.

Type C

Type F

Saint Barthélemy

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

Type C

Type E