I have never heard the term "footprint" before in this context. I would call this sheet a "groundcloth". The footprint of a tent, to me, is the area that it covers on the ground.
I think that a footprint/groundcloth is cheap and sacrificial. It exists to protect the tent floor from rocks and sticks and has little to do with keeping anything dry.
I do the same thing with my home ice rink. I save an old liner (no longer watertight) to go underneath and protect the new liner from tears.
I would advise getting a footprint/groundcloth slightly smaller than the tent so that it collects as little water as possible. Rolling up the edges of a larger piece of material to get it out of the rain is OK, but this creates the possibility of water pooling up in it.