I don't really care for the "fake news" label since it's so politically charged. But I would say a thing is a "fake fact" - a falsehood, to speak plainly - if it asserts a claim about the world which has no support from the scientific community (or worse, is actively disputed by the scientific community).
In other words if it's not grounded in empiricism it's a "fake fact."
In other words if it's not grounded in empiricism it's a "fake fact."