That would make a nice sized run for a few hens, with a 5' or 6' fence. In your climate, all they need for a coop is a 3 sided shed facing downwind -- and even that is mostly for comfort, and to keep the feed dry. If you want the coop predator proof, I would cover the 4th side with hardware cloth. You will probably want to put something like hardware cloth up the sides of the garden fence a couple of feet, also to discourage predators; You might also consider whether you have any predators that will dig under. The easy way to prevent that is lay hardware cloth along the lower edge of the fence on the outside, and find a way to fasten it to the fence. If you pin it down with staples or something, you will probably be able to mow over it once the grass grows up into it.
There may be other fencing that will work; lots of threads in this forum discuss fencing. You have to consider how small a hole your predators can get through, and whether it is strong enough.
It doesn't look like the area is fenced now, in the pic. One thing to consider is that it should be well drained, or your chickens will live in a muddy, stinky mess. Also, although they will eat all the grass is a fairly short time, they will love doing this if you choose a grassy area.