Yes, hardware cloth. A determined raccoon can rip through chicken wire. They can also reach through an grab chickens and attempt to pull them through larger wire. Not to mention they are skilled climbers, so you have to keep their run covered. I have hardware cloth covering all the windows on my coop. They are locked in at night so I don't worry too much about raccoons.
I'd use 14 gauge welded wire and 1/2" hardware cloth anywhere a raccoon could reach in and grab a bird. If your enclosure isn't that large, I'd just use the hardware cloth (it's relatively more expensive). Definitely don't use the chicken wire. Good luck!
We use the 1/2" hardware cloth on all coop openings like windows and vents, too. It's strong enough that they can't tear it, welded so they can't stretch a hole in it and has openings small enough that they can't reach through and pull parts of a chicken through. Gross, but they do it sometimes.
It's attached with screws that go through washers. If you just use a staple gun, they can tear it off. Some people screw through a strip of wood, too. It's good to attach your hardware with wood screws, too. Get good latches or a lock that they can't open, too. They are really good with those little paws and will fiddle with latches until they eventually get them open.
I have coons and I have found the best way is to lock the chickens in a building each night and keep the livetraps set. Eventually you will knock the population down. They are super easy to trap.
Coons can dig like a dog, rip wire and climb.
Anything 1/2" or larger they can reach in with front paws.
They are like cats in the fact that they can squeeze theirventire body through very,VERY small spaces. They use widowed to judge space. I raised a red and a blonde raccoon in the past, both females. Thevred was content staying where she belonged. The blonde was super calm, sweet, ame, but could get herself through the smallest of spaces! If your hand can squeeze into a hole so can they. Average sized can of tomatoes is enough for a head & very much so for a hand & arm.
Problem solving ability of a 3 year old child. Latches, clasps, levers are no problem for them. A latch that has to be moved in two directions to open will stop them. The clasps like on dog leashes are no problem for a coon to open.