So riddle me this, why are you trying to devise something that 'foxes' can't navigate when you admit cats are also a problem?
I feel confident in saying if a chicken can get through a tunnel maze or opening, so can every average sized cat with ease...
Also I highly doubt you will find many chickens willing to even try navigating a tunnel, let along a maze of tunnels, especially since they are nearly blind in the absence of light as would be the case the minute they entered the tunnel... My guess is the first chicken you could convince (or force) to enter a tunnel would freeze, (best case) stress and die (likely) inside said tunnel before they successfully navigated...
Chicken wire will not afford and sustained assault, a K9 (dog, coyote, wolf or even a fox) or many other larger predators can tear through chicken wire in a few minutes or less, or just bulldoze it down or climb over it...