If you really want to save this tree, I suggest you get an arborist with proper certifications (not just a guy with a bucket truck) to look at it and advise you. As far as plants under an oak, all shade tolerant plants should be fine under oaks. In zone 7, the choices are enormous.

Whatever you do...do NOT add potting soil or a little fence around the tree. Trees do not like water or dirt around their trunk. Check to make sure no one ever did this in the past.

Planting around the tree is tricky...if you aren't careful you could damage the roots. Most spring ephemerals (daffodils, Virginia blue bells, Trillium) should be fine.

Does the driveway drain properly? If water puddles round the tree you could add storm drains or french drains...although once again, you have to do this without hurting the tree's roots. You could remove a section of driveway to give the tree's roots more room to spread.

I would agree with laceyvail in that a trained arborist should come in and have a look. While trees live a long time, they do have a life span. But then again it may just need a trimming. In re: to plants around the base I would use something like pachysandra or Lily of the Valley which will spread on their own over time. This way you don't have to do a lot of digging around the roots. Or you could choose a few hosta that get big, so you'll only need a few to fill in around the tree. HTH

Don't know about zone 7 oaks, but the oaks I'm familiar with have deep roots and are ideal for shade gardens that involve many, many different plants that like shade. Digging around any of the oaks I know would not present a problem. You're only digging small holes to set in perennials or bulbs.