You Do Need power plug adapter while traveling from Palestine 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 Palestine are C and H. This is how they look like.

Palestine

In Palestine, outlets of type C and H are in use.

Type C

Type H

Saint Barthélemy

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

Type C

Type E