In a teacher's supply store I found 'Infostrip'.
It comes in 2" X 6' rolls with 'post-it' type gum on both surfaces.

Here is a link that might be useful: Tac-On

There are a number of acid free double sided tapes available in craft and hobby stores.
For a frame, you can buy molding strips (stain/paint to your liking) from a home improvement store and just miter and glue the edges since there will be no glass or structural strength required.
Tape the parchment to the wall and mount the frame around it with double sided tape that will take the weight.

It seems to me that the drawing is not going to look good on the wall unless it's laminated to something to make it reasonably flat. Normally, a frame shop would dry-mount it to foamcore board. Since I doubt you can get foamcore in a 7' length, you need to find something else. Masonite comes to mind, as you could go buy a 4 x 8 sheet and have the yard or Home Depot cut it to size for you. I'd then stiffen that by gluing some 1 x 1 strips to back, recessed from the sides, to create a floating effect on the wall. Then you could use some of the double sided tape suggested above, or perhaps spray adhesive (depending on how permanent you want this or how precious the drawing is) to mount it to the backing. If you still want a frame around it, do as suggested above; buy suitable molding at Home Depot or wherever and miter the corners.