Another prompt, not sure where it would go: Harry and Fleur meet during the Quidditch World Cup.
During the day before, to be precise, while browsing things to buy. Both love Quidditch and are fans. They meet and strike up a conversation, maybe about brooms or manoeuvres. To their mutual delight they find that the other is just as much of a fan as the other. Together they geek out. To their further delight, they sit in the same box.
After the Cup, they keep writing to each other, both happy for another friend. When the delegations come to Hogwarts, the two friends are very happy and immediately start a debate. Harry's teammates join up, Durmstrang students join up. When the Champions are selected, all four of them are Quidditch fanatics. This probably leads to interschool pick-up games, friendships are formed.