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

Here is Why You Need An Adapter

The outlet and plug type used in Saudi Arabia is G 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

Saudi Arabia

In Saudi Arabia, outlets of type G are in use.

Type G