In my experience,foxes won't go for cats. At the moment,and for the last year,I live right next to a graveyard in Kingston,London. Foxes are prevalent and are always over the fence where Bob (my cat) hunts.
As for fox-proofing the chicken house,nail steel mesh to the underside and make sure the door is closed at dusk and a latch fitted. Most shop-bought coops will be strong enough to keep out the foxes,I guess it's just the daylight foxes you have to worry about......... Ree