It is true that raccoons cannot jump.
However they can climb like you wouldn't believe. If there is ANYthing they can POSSIBLY snag a claw into to get a foothold, they will, and go up and over.
Also, while *raccoons* can't jump, dogs and coyotes and foxes most certainly can, so just making the bottom 3' of a run climbproof is pretty pointless.
It should be possible to make a pretty predatorproof run fence by applying a seamless piece of 2' wide flashing along the top of a 5' fence (so the fence is just mesh up to 3' and then from 3' to 5' has the flashing applied on the outside)... zoos do this sort of thing, although using very expensive clear plastics rather than flashing. HOWEVER it is going to catch one heck of a lot of wind and require a whole new level of strength-in-run-fence, and also be ugly as sin. While not protecting against owls or hawks. So I question the pointfulness. But it could be done in principle, and as long as there is nothing *else* a coon can use to climb up and over (e.g. the coop itself, or trees) it would likely work pretty well.
Pat