Chicken wire is just to keep the chickens in - it doesn't do much about keeping things out that want in. Lots of critters can chew through it and, as you found out, snakes can slither through it. You can't eliminated the predators; however, you can mitigate loss.
We have 1/4" hardware cloth around the coop and also around the pen. We buried wire perpendicular to the hardware cloth so nothing could dig under the coop or the pen. The coop is fully enclosed in hardware cloth and it's a virtual Fort Knox when we lock the door.
We have the 4' hardware cloth (the widest we could get) around the pen with 4' chicken wire on top of it to make an 8' fence (the local Tractor Supply had 10' T-Posts someone ordered and didn't want and they were cheap so we loaded up on them) . We used bailing twine to sew the two sections together so nothing could climb between them. Then, because we have a chicken hawk problem, we put
netting over the entire pen.
That doesn't mean we're snake-free. They can still find ways to get into the pen and we keep the coop door open during the day. We keep a
snake grabber in the pen and also on the front porch. And a shotgun by the front door of the house.
I shut my birds up in the coop every night and one evening about dusk the Guineas wouldn't go to roost. They kept walking around the front of the coop making their little whistling noises (I have a baby monitor in the coop). I walked out to the coop and my nervous darlings were gathered by the door. The hens were on roost. I saw the rat snake on the floor by the back of the coop. I grabbed my snake grabber, got the snake, walked by the house to get the shotgun, and the Guineas were sound asleep on their roost by the time I put the snake grabber back in the coop.
Snakes can be anywhere they want on the ranch with the exception of being within 10 yards of the coop. I don't care of they're in the barn or even in the garage because they help control the field mice. I don't even care if they're on the front porch (not completely true - I care if they're venomous and I'll tote them down to the lake with the snake grabber.....) Just stay away from my birds!