As far as papers go newsprint is probably the most environmentally friendly paper there is. It can be produced from a wide range of wood pulp, uses the least amount of chemical bleaches or agents to change the consistency or quality. In the US over 90% of newsprint is created from recycled paper.
In addition repurposing a newspaper that is bound for the landfill is going to be much more sustainable than using a plastic or laminated paper container that many foods use. I am sure there are more sustainable options but none of them are likely to be as convenient or easy to attain and use as an old newspaper.
That does not mean that the newspaper is safe. Some inks used in printing are quite dangerous to ingest. It is not likely to be the most sanitary option either as it may have been handled by many people and thus contaminated by any bacteria on their hands. It the newsprint was unprinted and freshly used it is likely as safe as any for wrapping food. But the paper is very porous so any liquids it comes in contact with are liable to bleed through to your food.