I don't know much about Jeane Dixon, so I can't answer specifically about her, but I can talk about fortune-telling in general.
Fortune-telling and prophecy outside of what God has revealed - first of all, is it possible? In a word, no. Now, to clarify, fortune-telling is common to many ancient religions and spiritism, but there are two kinds:
The more common one is essentially guesswork, either based on trickery (often employed by modern psychics), vague predictions that can easily mean different things (sadly many charismatics are guilty of this), or generic predictions that are fueled by the law of averages (eg. to say that there will war next year. There's always war). I think often, fortune tellers will employ all methods and so are able to give an appearance of being able to predict the future. But it's essentially deception and guesswork, and we know, statistically, if you make enough claims, something is likely to seem to appear true.
Then there's the second type of fortune-telling, which is full-on divination and the occult, where they do communicate with the demonic. Demon possession and the influence of evil is real. Demons do have insight into things that we do not, and so, revelation of some kind through the demonic is possible. But! Although demons are powerful, they are not omniscient. They cannot know or reveal the future through their own power or means. Only God knows the future. They can, however, deceive people, which is in accordance with their nature.
I think the line between guesswork and divination is blurred and it comes in different degrees, but we can and should consider it all evil. It's all divination, strictly forbidden by Scriptures. It's inherently evil and false, and so we can readily disregard and reject all kinds of fortune-telling.
Specifically, about the end of the world, this is what Jesus plainly says: "But concerning that day or that hour, no one knows, not even the angels in heaven, nor the Son, but only the Father."