I keep seeing this question, and people always rattle off the same few nineteenth-century names. But if we're talking about influence on what we consider 'modern' literature—the stuff that shaped the twentieth century and what came after—my vote is for Marcel Proust and Gustave Flaubert. Proust's 'In Search of Lost Time' didn't just tell a story; it built a whole universe out of memory and perception. The way he stretched a single sensation, like the taste of a madeleine, into a philosophical exploration of time itself... that cracked the novel form wide open for everyone who followed. Modernists like Woolf and Joyce owe him a huge, unpayable debt. It's not an easy read, but you can't understand stream-of-consciousness without him.
Then there's Flaubert. 'Madame Bovary' gets credit for realism, but his real gift to modern lit was the idea of the 'mot juste'—the perfect word. He treated prose with the precision of poetry, and that obsession with form, that author-as-craftsman model, influenced everyone from Henry James to Nabokov. He showed that how you tell a story is as important as the story itself, which is a cornerstone of modern literary aesthetics. Later French thinkers like Roland Barthes even built theories around his work.
Honestly, though, I think we sometimes overlook the influence of someone like Baudelaire. He wasn't a novelist, but 'Les Fleurs du mal' introduced the modern, alienated urban consciousness—the flâneur wandering the city, finding beauty in decay. That sensibility seeped into fiction through symbolism and later existentialist writing. His shadow is long.