If they are grapes, they should be edible. I suggest you check the seeds inside the fruit and compare them to other grapes. There are a few climbing plants that grow in the same area. They make blue fruit, but the seed inside is not grape-like.

Some sources warn against confusing moonseed, Menispermum canadense, with grapes. Moonseed is very poisonous but has only a single distinctive crescent moon shaped seed in each fruit. I think the plant looks very different than a grape.....but it really depends on how familiar you are with wild plants. Check and make sure you can tell the differences. Wild grapes have more than one seed in most fruits and they are not shaped at all like the seeds of the moonseed plant.

Here is a link that might be useful: Moonseed drawing, etc.

Heres a link for grapes so you can see what they look like and a link below to compare with moonseed.
grape leaves have toothed edges, moon seed doesnt.Grapes grow in downward clusters, it shows moonseed growing in very small bunches.

Here is a link that might be useful: grapes

They do look very much like grapes. Scroll down for the picture.

here are the leaves.
http://www.biology.duke.edu/dnhs/pics/Moonseed.jpg

Here is a link that might be useful: moonseed fruit

You likely have found Fox Grapes. They are wild and used to be plentiful along the Blue Ridge. They make delicious jelly and are dark red, strongly flavored grapes, generally growing on vines way up in the trees. GREAT jelly!