Thank you. May I ask why I would need another layer of chicken wire? Is it just for extra protection? I’m all new to this!
Most predators I can think of will go through that chicken wire like it isn't even there. It might keep out hawks, and that's about it. Also, it's secured to the wood with staples - a raccoon or dog will rip those right out. When you secure 1/2" 19 gage hardware cloth over every open air surface (my recommendation for a top level security coop - basically everywhere your chicken wire is now), use radial washers and screws to secure the hardware cloth to the wood. Or metal zip ties can work if they're tight to the wood or another surface. Any crack with a dimension larger than half an inch can let in predators.
For the poky or sharp parts, consider wrapping them with housewrap or old feed bags - it's the same material, super durable, and a couple thicknesses can help take the pokiness out. I've also seen folks split a garden hose lengthwise, and shove it onto sharp metal roof panel overhang. Foam is out because the chickens will eat it. They will also eat caulk if they can get to it. Rubber stall mats or similar type hard rubber can be used in some areas if needed.
To be fair, if you have a livestock guardian dog, or especially an electric fence wire running around outside the coop, that will keep predators away also, it would increase your protection if you had hotwire and then added 1"x2" welded wire everywhere the chicken wire is currently, like the previous poster said, and keep out the larger predators.
I'd definitely add at least a 1/2" hardware cloth apron (2 ft or more wide), and hardware cloth a few feet up the sides. In addition to addressing the gaps at the doors, as previous poster said. This would give you the basis of a mid-level security coop.
Are these livestock or pets? How strongly must you keep them safe? Must they be absolutely top level safe - can't tolerate any predator losses at all, or are you willing to tolerate the possibility of a few or more losses?
Weigh how okay you are with predator loss vs. the cost to create a mid-level or top-level protection coop, and then you'll know what to do. Everyone's answer is different - there's no one right answer here. Once you pick your level of comfort with predator loss, we can help you meet that. The predator load in your area and types of predators in your area also may influence your answer here, and once you get chickens, you may find predators coming around you never knew were in your area. Many of us have game cameras to keep tabs on things when we're not around.