This is the problem with AC:CF, the grass erodes too quickly. To grow the grass back you can plant lots of trees and flowers in that area where there isn't much grass and after a few days of the plants being there you should be able to see some little grass patches growing around them. Another way is not to walk over that area for a huge amount of time, and the grass should start growing back. I think the plant-method is a bit easier if you have to walk over that area almost every day.