You Do Need power plug adapter while traveling from Monaco to Faroe Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K and in Monaco are C, E and F. This is how they look like.

Monaco

In Monaco, outlets of type C, E and F are in use.

Type C

Type E

Type F

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K