Wow ! Yuck! What a PITA!
I'm going to assume that these
curtains are really old in the first place, which would be why it tore so easily. If this is the case, you've got a couple of issues you're going to be fighting, when trying to repair it. As older curtains get really brittle, the safty pins may not work, they might just pull right through the fabric. I would try the
safety pins , placing them as close together as 3 inches at the most. I would also whip the leading edge,< onstage> through all the layers, with a heavy thread, putting the stitches as close together as possible. Even with the saftey pins I would go ahead and whip as much of the seam as possible. The more points of contact between the two seperate pieces will reduce the stress on each individual stitch, thus reducing the chance that any one individual pin or stitch will pull through the edge on the rotten fabric.
One more thing that might help, if these are going to be trashed anyway, then go to the store and buy some "iron-on" patches. Iron them onto the upstage side of the curtain, every so often, these will assist in gripping the curtain fibers as much as possible. These would be in addition to the stitching
I hope that helps.