If you want to assure that it is fox proof, you will need a top on it. This can be solid or made out of wire. I suggest something stronger than normal chicken wire, since a fox, raccoon, or whatever can tear it or untwist the twisted connections. 2" x 4" welded wire is probably your most economical option, but many other things can work.
If you do put a top on it, you will be a lot happier if it is high enough that you can walk under it without hitting your head. Don't ask how I know that so well.
One problem with a 15' x 15' covered run is that you need some pretty good bracing to span that distance. Most of us need to consider snow and ice loads as well as wind, so the top bracing needs to be fairly substantial. One way to help yourself with this problem is to set a post higher than 6 feet right in the middle and run your bracing to that. That way you can put a peak on your top to make it easier to work under it and cut the span length. If you do go with a solid roof, it needs to be sloped so water runs off, otherwise it is almost guaranteed to leak.
Instead of using paving stones, I suggest you use a wire apron. Place an 18" to 24" section wide wire fencing all around the bottom of you run and coop. Lay it horizontal and connect it to the bottom of your fence or coop. You don't really have to bury it, but a lot of people remove a couple of inches of sod, lay the wire, and put the sod back. The idea is that the predator goes up to the barrier fence, starts to dig, hits the wire, and does not know to back up. With paving slabs you give them a physical barrier they can see, so you might be telling them where to start digging. Again, the 2' x 4" welded wire works real well for the apron.
Good luck!
