FIG. 1 is a front elevation view of a curtain fastening device showing my new design, the back elevation view being a mirror image; FIG. 2 is a left elevation view thereof; FIG. 3 is a right side elevation view thereof; FIG. 4 is a top view thereof, the bottom view being a mirror image; and, FIG. 5 is a top-front-left side perspective view thereof.