When we built our first coop and run, we knew that there were predators in the area but we hadn't seen any. Fast forward a year, and we regularly see raccoons, possum, cats, foxes and coyotes. As was said in a movie, "Build it and they will come."
We didn't cover the floor of the run with wire. What we did do, however, was to extend the welded wire walls of the run downward 6" into the soil and flared them outward 1-2 feet as a skirt. Then, on top of this skirt we stacked field stone and old bricks about 1.5 feet high. We took this approach as a result of the type of soil we had, budget considerations in and the numerous rocks we had all over the place. Basically, we did what we could in the situation we are in, using available materials. I'll recommend that you do more than you think you should, as a precaution. If that means using hardware cloth on the floor of the run, then I'd do it. Chicken wire keeps chickens in, not predators out.
While ours might not be the perfect design, we do have a den of coyote pups about 150 feet from the run (just found this out) and have not had any losses. I figure that they are going for easier food sources. Come to think of it, there are hardly any feral cats around anymore. Once that runs out, chicken will become more attractive and I believe that we are ready for that possibility.