Trial and error will lead you to the best frame. For a formal effect, try a copper or gold frame. Simple black may also work with your photo. A beige mat surrounding the photo will help to set off the photo and bring out details in the picture.
The best color frame for sepia tone photos is a warm, chocolate brown because it brings out the contrast. Cream or beige is also good for the same reason.
The brown hues in a sepia tone photograph are compatible with many shades of wood frames. Also, old-fashioned and ornate frames can be compatible with sepia photographs depending on the subject of the photos.
You will want something the offsets the reddish or brown tones of the picture (thus, red and brown frames are poor choices). A solid navy blue, bold forest green, or black frame will all offer enough contrast with the picture colors to make a pleasing combination. You could also try a metallic silver frame.