If you want to incorporate a landscaped area along your fence, mulching the beds helps to suppress weeds in the area. You typically need about 2 to 3 inches of mulch to stop weeds from germinating.
I recently moved into a new house with a wonderful, fully fenced-in backyard. The downside? Keeping that fence line clean! Grass and other weeds grow up from under the fence and creep into my yard ...