Unfortunately, Paul Valéry wasn't around long enough to sport black turtlenecks and free associate en français about power and difference and babies in front of mirrors, so he's not the most popular Frenchie in English departments these days. Don't underestimate him, though—he had some serious cred back in his day.
Valéry was a distinguished and accomplished fellow, a poet, essayist, and critic all rolled into one. He was a humanist—someone who believes in the importance of human beings over institutions, has faith that humans actually have some power over what they do, and is sure that such a thing as "human nature" exists.
Let's put it this way: Valéry probably would not have appreciated having an English professor coming up and telling him that deep down, he, like everyone else, was a social construction.
Valéry had some serious self-discipline, dedicating himself fully to the "Idol of the Intellect" through the endless study of human consciousness and the nature of language. He believed that emotions were just too messy and distracting—they just got in the way of clear thinking. And clear thinking was what was most important to Valéry.
This dude liked to record his ideas as aphorisms, which were collected and published in his Cahiers, or "Notebooks," which clocked in at over 20,000 pages. Writing these little maxims was a huge source of gratification for Valéry; as he put it: "Having dedicated those hours to the life of the mind, I thereby earn the right to be stupid for the rest of the day" (source). We didn't make that up.
Valéry was fascinated and preoccupied with the human mind, and he used the work of Leonardo da Vinci to study how the unlimited, brilliant ideas formulated in the mind do not necessarily translate perfectly into action. Is that because the human mind is more boundless than reality, or is it because we just haven't figured out how to implement all our crazy ideas yet?
Valéry wrote essays on everything from philosophy to dance to architecture to politics, but at base, he was always considering the value and meaning of the human experience. He liked to sit around and ponder human intellect and human sensual experience, and he insisted that his aim was "to advance towards knowledge, through a multitude of questions and precautions" (source). If it sounds vague and abstract, that's because it is.
It may sound minor, but Valéry was totally sensitive to dramatic weather: a wild thunderstorm once scared the bejesus out of him, and that made him rethink his priorities and abandon the study of literature for twenty years. Instead, he moved on to mathematics and philosophy, which apparently had a much more calming effect on him.
When Valéry finally did pick up his pen again after twenty years, he wrote about authors like Edgar Allan Poe (his favorite), Descartes, Mallarmé, and André Gide. Valéry was fascinated by the power of words and the mystery of art. He also spent 25 hours a day, 8 days a week thinking about what an author means in a work versus how a reader reads that same piece.
Bottom line: this dude has put some serious thought into the study of literature. So put on your thinking cap, and get ready for it to get real.