You Do Need power plug adapter while traveling from South Korea 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 South Korea is F. This is how they look like.

South Korea

In South Korea, outlets of type F are in use.

Type F

Saint Barthélemy

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

Type C

Type E