Although Nostradamus (and many of his adherents) believed he could see the future, Nostradamus was a man of his times who was influenced by the popular concepts and culture of the day. He was a student right before the time when astrology and astronomy were considered core subjects; he studied medicine; and was an apothecary during the plague.
The concepts that likely had a profound influence on Nostradamus include:
Astrology: This is the study of the movement of stars and planets with the idea that these motions are related to the people and events on Earth. By knowing the charts and positions of these celestial bodies, supporters of astrology believe that future events can be predicted.
Alchemy: This secretive study focuses on the process where you're supposed to be able to change any metal into gold to give you material wealth and achieve the ultimate goal — the Philosopher's Stone, a stone that provides immortality.
Medicine: Doctors of the time were educated in a mixture of state-of-the-art medicine (looking at body fluids), basic anatomy, some astrology, and folk medicine. But treatments were limited to herbal concoctions and using leeches to bleed out the illness in a patient, who often wasn't much better off for the help. Toward the end of the Renaissance, using observation to investigate how the body worked took hold.
Humanism: This is a Renaissance belief that people should focus on all things human, especially exploring their capabilities. Beauty created by people in the form of music, art, and literature was valued specifically because it was a human creation. Humans have a natural dignity and value because they're people. People can realize their potential by using logic and thinking critically about the world rather than relying on faith.