I would consider a new fence or adding electric - a GSD seeing something interesting on the other side can jump that with ease, even if your chickens stay on your side.
We have field fencing, with slightly smaller openings on the bottom than on the top and about the same height as yours. The chickens could have gone through it when they were younger, but only one did, one single time. I trained my chickens to come when called so it wasn't a big deal. They have never gone over it - maybe because they are all dual purpose breed and pretty large, or maybe because there is enough space and greens inside the fenced area, so they don't feel like they need to bother at all.
A fox or small bobcat, however, could walk right through the fence, before my dog has much of a chance to notice. We will be getting a no climb fence (woven wire, 2x4 openings) installed very soon, 6ft, 2 extra wires above to keep out deer, too. I would never trust that fence to keep my chickens safe from large dogs...