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

Here is Why You Need An Adapter

The outlet and plug type used in Italy 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

Italy

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

Type C

Type F

Type L