If the fascia is attached with screws near the bottom, then you could pin the plastic between the 2 boards without puncturing it. I think that any wooden overhang which extends back over the roof, creating a little overhang, will immediately be converted into housing by the
local creatures who will appreciate a high and dry home, and they will start chewing up the plastic in short order.
While more involved, I would suggest making a wooden cap from boards (viewed from the side, would look like an upside-down U) which would slide down over the primary board that caps off the soil. So you would have an upright board and the plastic comes up over and down to cover that, and then this wooden cap sits down on top and covers the plastic, holds it in place with just gravity no screws, and doesn't provide habitat for unwanted guests. You can cut a miter edge and then attach fascia below that with a matching miter, so rain will drip out and away. I'm attaching a quick napkin version of what I mean, the cap could be made by nailing 3 boards together so they can slide over the top. I hope it makes sense!
Edited for monster picture size!