After the war, Harry can't stand being alone at Grimmauld so he moves into a flat in a side road of Diagon. He finds out that Fleur lives next door after her divorce, but due to different social circles and work hours, they don't really connect. For a while, Harry had a fwb thing with Padma, who introduced him to a whole new world of tastes and spices before she had to move away for a job in Finland (or wherever else). So now he's trying out new dishes whenever he can.
One day, he's in the middle of cooking some Thai dish when Fleur knocks on the door, intrigued by the smell. Harry offers her a portion, but he has to get back to the kitchen. Fleur follows him and they end up catching up while Harry completes the dish. They eat it with some social lubricant wine and afterwards Harry invites her to stay for tea. There Harry is shocked by Fleur's sacrilege of dipping biscuits into her tea until they are soaked and almost breaking apart while Fleur cannot understand why you'd want to put milk in your tea. They banter back and forth and suddenly the sun has set and it's 10pm.
Fleur ends up coming by for food more often and they end up spending those evenings together. Over a few weeks, touches become more frequent and longer, goodbye kisses on the cheek tend to linger and so on. So Harry isn't surprised when they start making out after he served some Khanom Krok (Sweet Coconut Pudding).