Nietzsche was a proto-modernist—that is to say, a forerunner of modernism, in that, like Marx and Freud, he was a "master of suspicion." What this means is that he didn't take contemporary culture and society at face value; he wanted to dig beneath their civilized surface to reveal something altogether darker and more disturbing.
Just as Marx strove throughout his whole adult life to reveal the cruelty and exploitation of the capitalist system, and just as Freud set out to expose the primitive psychological drives buried deep within the human subconscious, so Nietzsche sought to challenge the commonplaces of contemporary Western society by exposing the decaying foundations of its cultural life.
Nietzsche was pretty scathing of the notion, almost universally shared in his day, that human progress was not just inevitable, but desirable. Huge strides in science and technology had made nineteenth-century man very sure of himself, giving him a sense that there was nothing about himself and the world around him that he couldn't know. Scientific ideas such as Darwin's theory of evolution by natural selection had painted a picture of man as slowly but surely evolving over time into a superior being.
Nietzsche didn't reject Darwin's theory on scientific grounds. What he objected to was what he saw as its unwarranted application to the cultural realm. Far from representing an advance on what had gone before, nineteenth-century culture for Nietzsche displayed unmistakable signs of degeneracy. He compared contemporary Western culture, infused as it was with the spirit of democracy (which Nietzsche despised) and scientism (the belief that science could explain everything) with the great ages of cultural achievement, such as the Renaissance in Italy and France under Louis XIV, and found it wanting.
Though Nietzsche would almost certainly have regarded modernism as a regrettable by-product of Western man's continued cultural decline, he would've shared its commitment to radical social critique as a means of uncovering the often sordid reality of contemporary society as well as recovering the shattered fragments of a vanished European high culture.