Any of Hans Christian Andersen's Fairy Tales and Stories is an obvious starting point — the standard English translation by Tiina Nunnally captures the wry, sometimes savage tone of the originals, which is largely lost in the Disneyfied versions most people know. The Improvisatore, his most autobiographical novel, gives a more direct sense of the man behind the stories.
For Funen as a place, Johannes V. Jensen's The Long Journey — a Nobel-winning prose epic from the 1920s — uses the island and its people as the cradle of Nordic civilisation. And Carsten Jensen's We, the Drowned, set partly on Funen and on the seas to which Funen sailors went, is the best Danish novel of recent decades.