Can Heavy Storm destroy a Field Card if Field Barrier is in play?

No. If Field Barrier is on the field, the Field Spell Card will be unaffected by the effect of Heavy Storm.Because Heavy Storm destroys all Spell and Trap Cards simultaneously, Field Barrier acts as a shield for the Field Spell Card, preventing it from being destroyed.

To destroy the Field Spell Card, the Player must destroy Field Barrier FIRST. Effects that supposedly destroy both at the same time, such as Heavy Storm and Harpie's Feather Duster, do not affect the Field Spell Card.