Um, that is more than a bit scary!
You SHOULD be able to predator proof the coop. 1/2" hardware cloth over all openings, fixed with screws and battens or poultry/fence staples NOT Arrow style staple gun staples (other than for positioning). If you also have larger predators, 2x4 welded wire as well. Use poultry/fence staples on the 2x4 wire fencing. The small ones can't get through the HC that the big ones could possibly rip and the big ones can't get through the 2x4 fencing since it is larger wire. Put the 2x4 over the top of the HC on the outside or put the HC on the inside of the openings and the 2x4 on the outside. That way bigger predators will have a tough time getting to the HC so there is less possibility of it being ripped (unnoticed) leaving an opening for smaller predators like weasels.
If you have bear problems: I've read that people use hotwire fixed on or close to the coop. Bears raid bird feeders so if you store scratch or BOSS in part of the coop/run area, don't. 
 
The run is harder since it doesn't have a solid roof but still possible. The free range area? You are right, a fence is just a deterrent and means nothing to avian predators.