If the grape was in the tree, chances are it isn't getting enough sun on the ground. That's the first problem to solve - full sun without competition or it will be right back up that tree.
Find where the grape vine is rooted, pick a main trunk and cut it back to the height of the fence. Then choose lateral branches that come off both sides of that main trunk and line up with the fence boards. Cut everything else off. Then cut your chosen laterals back to 3 or 4 buds and secure them to the fence boards. As the buds grow, you will have to keep securing them to the fence boards. Next winter, to encourage fruit production, cut it back the same way and cut everything else off. To cover the fence, let your chosen laterals grow and cut everything else off. Prune the braches off the laterals back to just one or two buds.
Daisy