Prior to attending Hogwarts, Harry's best example at a healthy functioning relationship between two adults is that of the 1991 film, The Addams Family. So whenever he gets around to wanting a romantic relationship, he goes from being (a justifiably) shy and mopey kid to copying Gomez Addams trying to find his Morticia. Fleur otoh is looking for anyone who isn't affected by her allure. Friend are hard to come by due to the jealousy and notoriety of being close to a veela. She thinks that Harry's antics are more of a commentary about people's behavior around her and the entire situation. His antics are cute enough and so is he, so she goes along with it leading to silly scenes of Harry professing his love and Fleur overdramatically swooning.