After the second task, Fleur thinks about ways she can repay Harry, and after witnessing the trainwreck with him, Parvati and Cho at the Yule Ball, she decides to help Harry along in the field where he clearly needs the most help. Getting a girlfriend.
Not just anyone will do, she wants to do Harry a solid, after all he saved Gaby, so she starts with a list of all girls in his year and above, eliminating them one by one. Some are easy, Hermione is dating Krum for example, others require a little more thought. In the end, it comes down to Katie Bell, Tracey Davis and Sue Li. So Fleur observes them for a while, how/if they interact with Harry, tries to track down whether the gossip about them is just that and so on.
After a week of careful contemplation, Fleur decides that Katie Bell is the one for Harry. With that, phase 3 begins where she starts to engineer situations that result in the two spending time together. The attraction from both is clearly visible, but neither is making a move. After a fortnight where nothing happened, Fleur decides to fake them out into a date, sending invites in the name of the other to them. After the initial confusion, they enjoy the date, and quickly agree to a second one. Fleur then appears to offer Harry some advice, that results in the first kiss between Harry and Katie.
Fleur should be happy, mission accomplished. However, during the month she spent invested in this project, she might have developed a crush, on both of her labrats friends. Therefore, Fleur comes up with a new plan, Codename: Triangle.
Bonus points if Fleur thinks she is super sneaky and manipulative when in reality it is really obvious what she is doing to everyone other than Harry and Katie.