There is a film like Paper which is widely used as a substitute for paper coatings for packaging uses. It is a plastic film that is usually made of high density polyethylene (HDPE) in which high percentage of mineral masterbetts are added. In fact, calcium carbonate (CaCO3) gives it its soft feel and texture similar to paper.
Ideally, Paper Like film is grease and oil resistant and can be heat-sealed (given that it contains polyethylene). However, its rigidity and the way it folds are similar to paper.