Raccoons can chew through chicken wire. They can also be active during daylight hours as well. The raccoons that come to our property don’t care what time of day it is, I’ve seen them in the afternoon on sunny summer days. They climb and they chew. Securing only the bottom few feet of the run walls is just asking for trouble.
OP you mentioned string - so is your chicken door an auto door? If yes, is there a way to install it on the inside of the coop, so the string isn’t accessible from the outside? If you do that, and nail a small board across the bottom on the front, to make a lip overlapping the door’s bottom edge, the raccoons won’t be able to slip their hands underneath and pull the door up, and no string to grab either. I have an auto door with a string, too, but it’s mounted on the inside.