I recently had my basement water-proofed with a french drain and 2 sump pumps. They cut away the paneling about 2 feet from the ground up. Studs and foundation are both exposed. How do I "fix" the walls so that I can lay some carpeting down?

Try putting scrap paneling to fill in the cut areas. Make sure it's the same thinkness as the original stuff (any wood product the same thickness will do). Then either panel or drywall over the whole wall. Or since you have to remove all of the trim anyway, consider removing all the old cut paneling and replace with new paneling or sheetrock (depending on your skills).