You may want to get some buckram to add stiffness and strength to the top hem. Also, you may want to just sew it flat and use the curtain rings with alligator clips.

Here is a link that might be useful: curtain rings with clips

If you are a non sewer I would leave the curtains alone and just sew or buy blackout liners and hang them together on the rod with separate clip on rings. When you hang them put the ring from the curtain on first and then the one from the lining and so on all across but put the last 2 from the lining on at the end and then the last one from the curtain.

Put the side with the 2 blackout rings on the ends and the end of the curtain rod with 1 blackout end in the middle of the window. Doing it this way you avoid all the headaches of trying to sew them together and you can be sure the lining won't pull on the drapes. Putting the rings of the blackout inside ensures that it will not show.

If you have the material for the blackout lining then cut it an inch shorter in width and use only one ring on each end

An even easier way to line your draperies. Make panels of lining with doubled hem at top. Work button holes spaced approx. the lengths between your pleats across the hemmed top. Use drapery rods with hooks. Hang the panels by slipping buttonholes over hooks--then hang draperies on hooks. When you open and close, lining & drapery move together. You can get some slip pins to "tack" the fabric edges together so one doesn't drag behind. I read this tip many yrs ago, and have utilized it myself.