I tried to make do with a 4 foot chicken wire fence for a long time. They either got over it or under it. And it certainly did not prevent preadators from getting to them. The best thing is to use a higher and heaver gauge wire fencing such as a 2x4 grid which you can get at Lowe's. It's about $50 for 50 foot roll. ($1 per foot)
You have to anchor your corner posts (should be a 4x4 post) with cement. Then stretch the wire tight. In a pinch you can run a bar in and out of the wire holes and hook it up to a chain and pull it GENTLY and SLOWLY with a truck or other heavy equipment. (My fourwheeler couldn't pull it tight enough, not enough traction) then while the tension is on, nail the fencing to the other post.
This makes the bottom nice and tight along with the middle and top.
I had the same problem as you and tried running kite string from each metal post making the fence higher but they still were able to get over it.
All in all, if you can't build a new fence, clip their wings, remove anything they can get up on to get a vantage of jumping over, and use cheap metal stakes to hold down the bottom of the wire snug to the ground.