Harry and Fleur are time travelers. Or lovers separated by time.
But they are always separated through time because of how muddled the timeline has been from all the time traveling that occurred from parties wanting to change the outcome of the war. Hence, their (relationship) timeline becomes nonlinear and depends on how they are perceiving time.
In this universe, the veela are capable of looking into the future once at their maturity. Some use it to see their career, how many children they'll have, any kind of future is allowed. However, to the veela that uses it to see who their love is, that can get complicated. Which is why there is a fair warning not to see directly who you are going to fall in love with. But Fleur, wanting romance and true love more than anything, decides to peek into the future and sees, Harry Potter. In the "future" she sees herself drawing a watch on his wrist, with a promised date.
The story will be about the how she will be looking for him throughout time and space, and how he will be looking for her vice versa and how they will finally meet at that promised date only for a moment of fluff and romance, and how that reality will crumble.
The ending (or part of the ending) however is that they meet each other again finally no longer separated by time and space but they do not know each other (or have forgotten their time together) but somehow have a lingering feeling that they have seen lifetimes of each other. (Kimi no na wa style)