I have false but "useful" beliefs. Although I would more describe my beliefs as having truth to them.
I also have false beliefs which are simply delusions which I don't find useful. (I am only able to see that they are delusions after a long time has past and I can look back on them and see them for what they really are.)
So people with depression or low self esteem, for example, have "false and unhelpful" beliefs - such as "I am bad" or whatever. As a result, they tend to 'forget' all the evidence they are ok, and concentrate on all the evidence they are not. People with high self esteem often do the opposite thing. They focus on all the stuff that shows them in a positive light, and have a tendency to 'forget' (or minimise) those things that don't.
Neither of them are 'correct' views, are they? They're both distorted. It's just that one distortion is helpful to the person and the other is not.
There was a study I heard about on a documentary where they found that people who deny having a series of thoughts that it was suggested everybody has had at some point (so for instance "Sometimes I enjoy having a bowel movement" or "I have at some point fantasised about killing myself so that other people would feel guilty") were significantly more likely to be successful. The idea was that these thoughts are so common and universal that the participants were highly likely to be thinking them, but that they would later deny this to save their positive self image. Because they had a positive self image (but an essentially delusional one) they were more likely to be confident, and therefore more likely to succeed.