Raccoons can be kept out by two sizes of wire mesh.
One size keeps their little hands out (1/2" holes)
Or some bigger sizes keep out the body of the raccoon, but still let its hands reach in. If you use wire with that size holes, you need to keep it at least a foot away from where the chickens can go (so the raccoon's hands cannot reach the chickens). So that size wire starting at 3 feet up should be fine. It might not even need chicken wire over it.
One size keeps their little hands out (1/2" holes)
Or some bigger sizes keep out the body of the raccoon, but still let its hands reach in. If you use wire with that size holes, you need to keep it at least a foot away from where the chickens can go (so the raccoon's hands cannot reach the chickens). So that size wire starting at 3 feet up should be fine. It might not even need chicken wire over it.