The honor of being called founding fathers of modern poetry might be best shared between Walt Whitman and T. S. Eliot. Baudelaire, however, with the publication of Flowers of Evil in 1857, proved himself to be a poetic iconoclast and forerunner of many modern trends. He broke from the classicism of the Romantic poets by opening poetry up to previously forbidden subject matter—the rough underbelly of society, drugs and drink, sexual sadism and obsession, even Satanism. Baudelaire writes of love and beauty, but unlike Romantic poets, he includes darkness and evil as necessary parts of both.
The "Parisian Dream" section imagines a world devoid of nature and could be seen as a forerunner of surrealist imagery. We see other similar surrealist hints, such as in "The Blind," where the speaker, who has sight, is full of despair, but those who are sightless have hope.
What makes Baudelaire most influential to modern poetry is that no subject is too harsh, personal, or forbidden for him. We see this "there are no taboos" attitude burst open after Baudelaire, becoming accepted in the full flowering of what's called modern poetry. The examination of the human self and society in all its beauty as well as degradation is what Baudelaire first created poetically in Flowers of Evil, before modern poetry came to be called modern.