You Do Need power plug adapter while traveling from Isle of Man 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 Isle of Man are C and G. This is how they look like.

Isle of Man

In Isle of Man, outlets of type C and G are in use.

Type C

Type G

Saint Barthélemy

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

Type C

Type E