Idea: It started with pain After being attacked with the cruciatus during the third task/graveyard, neither Harry nor Fleur can sleep, so they have a late night conversation in the hospital wing and don't realise how the hours fly by. Think of it as one of those deep friendship bonding things.
So the next day they can finally sleep (still in the hospital wing) and Harry promptly gets a nightmare, which wakes Fleur and she helps Harry deal with it (throw in some Veela magic if you like).
This could go down a few different ways, but IMO the best would be for them to meet during the summer again and again. Harry has "human" contact, which helps him to deal with the graveyard.
Just imagine how the Dursleys would react if Fleur shows up at their doorstep. You could have their friendship include more and more banter, so that when the dementors show up and Fleur roasts them with a fireball, Harry just deadpans "that was hot". No underage magic warning, so Harry stays longer in Surrey (I don't think that he'd mind with Fleur around once she gets off from work) and eventually, the Order shows up, completely surprised by Fleur (maybe with Tonks being like "wait, you didn't notice the dropdead gorgeous girl hanging out with Harry for the past month?" and the other guards just awkwardly shuffling around).
For the romance arc, I'd say make it a fluent transition. More touches, hugs get longer, pecks on the cheek linger and so forth. This could lead to a few hilarious conversations along the lines of "so we're together now?" "yeah" "great, what do you want on your pizza".