cold weather kills fig tree
Simply prune out the deadwood. The new shoots will regenerate the plant. It will probably be bushier than the old tree. You can thin out some of the new shoots if you would like the new plant to be more tree-form.
You probably will not ripen any fruit on the bush this season. You should see figs set next year on the wood that is grown this season.
Please let me know if you have additional questions.