Although it was more of a cardboard thickness and too thick to wrap with, one option is to fold it into a box to still make use of the patterned print. There are lots of free templates available online to help you create a box. You could also carefully tear off the top layer of paper and glue it onto a scrap wood or cardboard for an instant box.
Dress up your packages with holiday nail decals, bows and tags. Small fake flowers make a great stand-in for bows.
Another tip for casting a warm glow on your mini Christmas scene are these candle sticks in the tips of mechanical pencils I found. I just knew they would be perfect for Christmas. They are very easy to trim and already come in brass-looking holders! You can leave the pencil lead in or replace with it with string or thread for wicks. (I chose to replace mine since I was working in a smaller scale.)
Happy holidays and have fun turning trash into Christmas treasures!