Pamela, you will need to test to see what the finsih is first. Take denatured alcohol on a small rag a place it on the finish in an area that will not show. If the finish melts it is shellac if not it is varnish or lacquer. You can only french polish with shallac. If the finish is shellac then yes you can polish the scratches out. If varnish or lacquer then try paste wax. I use Briwax in the color of the the wood. Varnish and lacquer is hard to repair.