You Do Need power plug adapter while traveling from Saint Barthélemy to Vatican City.

Here is Why You Need An Adapter

The outlet and plug type used in Vatican City are C, F and L 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

Vatican City

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L