Nostradamus did not foretell the future; he was a prophet not a seer. These two terms have become conflated in most of the Western World, and now we habitually refer to a prophet as someone who knows what will happen in the future. Being a prophet is only tangentially, and occasionally, related to predicting the future.
A prophet is a person who reveals Truth, a seer makes predictions. I should note here that Muslims still use the term correctly, Mohammad and Jesus were prophets of the Abrahamic faiths; they revealed Truth about God. Nostradamus is described as a prophet, yet people ascribe to him the ability to tell the future. But if he could actually forecast future events, why are his predictions so vague and obscure?
I know, he did it to prevent the Inquisition from imprisoning him. Or he did it so that only certain people would be able to interpret it. (Interestingly enough, only the people with books to sell.) Or maybe he was just a temporal cock tease.
I want to take a moment to deconstruct these arguments before I talk about what I think he actually did.
If he was so concerned about the Inquisition, why did he engage in herbology and astrology, both questionable activities in the eyes of an orthodox priesthood? If he was trying to be circumspect, he wasn't very good at it. He published the Centuries in his lifetime, and told the future of the Medici children for Queen Catherine and foretold the fate of Henri II. Not particularly advisable for someone who wanted to remain below the radar of the Church. Obviously he wasn't trying to hide from the Inquisition.
If he was trying to make certain that only certain people could understand what he was saying, I think that would be truly evil, and given his other works and descriptions of his personality, that sort of evil would be out of character for him. Why is it evil? Suppose you know something horrible is going to happen, but you only let a few people know rather broadcasting that information to a wide audience. If people die in an event that foreknowledge might have prevented, then the blood is on the hands of the person who kept it secret.
On a side note, never trust Nostradamus' translators; almost every one of them translates with an agenda, and makes sure that the prophecy says what they want it to say. I have read the Centuries in the original French, and trust me, they do not say what the translators make them say. There are obvious efforts to make them fit actual events and make it seem like they were stunning bits of prediction.
Finally, maybe he was just a tease. Maybe what he wrote was complete B.S. and he knew it, but this also seems out of character for the man.
Ascribing magic powers to Nostradamus completely belittles what I think was the man's true brilliance. Remember, prophecy is the revelation of Truth and that is what he did in the Centuries. He wasn't directly predicting the future; you can find the future in his writings, but you find it because it is a revelation, not a prediction.
His prophecy, his truth, lies in the fact that he created what amount to Jungian Archetypes of history. He revealed patterns in broad stokes. He identified events and circumstances that would lead to those events and created poetry to enframe those patterns. His foretelling of the future only works because of the cyclical nature of time.
If A happens the B is likely to follow.
When you look at Nostradamus through this filter, you see the true brilliance of the man.
What evidence do I have of this? As a physician, Nostradamus would be skilled in observing patterns of both illnesses and treatments. He would have possessed a rudimentary understanding of Scientific Methods. (Rudimentary only because Science in his day was still in it's infancy, and only beginning to separate from Alchemy and other mysticism.)
An example of this understanding of patterns can be found in the fact that he was possibly one of the first doctors to understand the linkage between cleanliness and illness. Many modern mystics like to claim that he discovered that link by looking into the future and seeing modern sanitation. I think it is far more likely that the man was just brilliant and had an insight into a primary cause of disease, brought on by keen observation. (And I would like to note how tired I am of people claiming that since our ancestors did not have modern technology that they couldn't do anything and had to rely on aliens or magic to accomplish their achievements.)
Nostradamus discovered patterns, and figured out how those patterns are interdependent. He then enframed the patterns in the only way he could in the 16th century; he cloaked them in mysticism. And today, we completely miss the point, we can't see beyond the mystical enframement.
And the problem is made far worse when that magical enframement is dumped on a group of people who have not got the means to understand the Truth underlying the prophecy. It feeds the ideas of living in the end times, it feeds the sense of doom, it feeds horror.
Prophecy works because people, whether or not they are conscious of it, make the prophecy come true. Science fiction is prophetic because it plants ideas into peoples' heads, not because it actually foretells the future. People make the future based on science fiction. For example, the flip phone would never have existed except for the communicator in Star Trek.
And that turns Nostradamus into a nightmare for the future. His prophecies are often dark and violent because human nature, especially in his time, is very dark and violent. And people who devoutly believe in his prophecies guide human events down that path. Nostradamus' prophecies tell the future simply because we make the future fit into what he wrote.
Prophecy doesn't predict the future, prophecy creates the future.