People often ask, "What is a good ground cover?" I always answer' "The term 'ground cover' usually equates to an invasive plant. Most of the ground cover plants we have used in the past have turned out to be invasive. English Ivy, periwinkle, vinca minor and major, chameleon plant and many more non-native plants have escaped cultivation and are spreading through ecosystems choking our native plants and altering forests.
Learn how to identify and control invasive ground cover plants.
In my article on landscaping a hillside, I show examples how we can use a mix of mostly native trees, shrubs, grasses and perennials to achieve ground coverage. Here is an article listing some mostly native plants that are good in such situations.
Another choice is utilizing a native grass mix. If your areas are in the full sun, you could do a native grass seed mix on the hillside. These grasses have deep root systems and are great at holding onto soil. You can order them here https://www.americanmeadows.com/products/southeast-native-grass-seed-mix . You can plant the seed then cover it with your erosion control fabric. Here are my articles covering the topics Covering Slopes, Mitigating Landslides and Native Grasses.