After being given a vague, not-at-all-helpful tip from Cedric, Harry goes to Myrtle's bathroom to take a bath with the golden egg. But when he gets there, he finds he's not the only one there
Right in front of him, in her bathing suit, is Fleur Delacour, who is currently being harassed by the angry ghost
After convincing Myrtle to leave her alone and give them some space, Harry asks if Fleur has had any luck with her egg. Fleur thanks him for helping her with Myrtle, and, after hesitating for a moment, decides to return his kindness with an honest answer.
She tells him that she hadn't had any luck with the egg herself, and Madame Maxime seemingly lost her patience and told her to listen to it underwater. He tells her that Cedric gave him a vague hint. Confused, she asks if Dumbledore is helping him like the other Headmasters are, and is surprised when he tells her that he isn't.
Giving him a look, Fleur tells him that isn't really fair. Harry shrugs, saying he's used to it. She tuts, before asking if he'd like to join her in the water to listen to the clue? That perhaps, between the two of them, they'd stand a better chance of figuring it out?
Harry can't stop the blush that spreads over his face at the thought of being in a bath with Fleur, regardless of the size and situation. She rolls her eyes, correctly guessing the reason behind his sudden blush, saying that it isn't any different that swimming in a pool together, and tells him to relax.
They dive into the water and listen to the clue, discussing it a bit afterwards. But as the night goes on, Fleur says that she better get back to the carriage before she's missed, asking if they can meet again tomorrow to discuss ideas for breathing underwater?
Harry easily agrees before watching her leave.
And that's how Harry and Fleur became unlikely allies in the tournament, as well as unlikely friends.