Note: I use the sortinghatchats system - +here’s (M to be safe) a link to their ‘basics’ post. To briefly summarize, though, they sort everyone on two different (and equally important) aspects of their personality: the first (your “primary” house) is why you do things, where the second (your “secondary” house) is how you do things. @starbuck asked me to sort my Fleur from English Lessons, so here I am.
Primary (the “why”)
Sidenote!Fleur is a Gryffindor primary (M):
Gryffindor Primaries trust their moral intuitions. They feel what's right in their gut, and that matters and guides them. If they don't listen to and act on that, it feels immoral.
I think there's a good argument for her being a Gryffindor primary in the books - she leaves her home to come fight in a foreign war in a country she doesn't have a particularly strong connection to, which feels more like a "felt" house (i.e., Gryffindor/Hufflepuff) to me than a "constructed" one (i.e., Ravenclaw/Slytherin) - basically, felt houses are about trusting their gut instincts, where constructed houses are more likely to consciously examine whether those gut feelings are correct.
I don't think that Fleur routinely steps back and dissects her gut instinct. She goes from spending 10 months at a Scottish boarding school that ended in tragedy to working at a bank in London - despite almost certainly believing that Voldemort had indeed come back. (Harry explicitly says that that's the case, and not only does she continue to be friendly with him through the end of GoF, she pretty much immediately gets involved with a man who was explicitly presented as Harry's family. Those are not the actions of someone who's weighing pros and cons or questioning her gut; that's the gut instinct of a felt primary.
And if the question is whether she's a Hufflepuff or a Gryffindor, I think she has to be a Gryffindor. Fleur does not care about social harmony if she is Right - you can see it in GoF in general as well as in her interactions with the Weasleys in HBP. Fleur is absolutely unwilling to give an inch or look at a different point of view - a Hufflepuff might have seen the core of Molly's concern and addressed it with empathy. I genuinely don't think it ever even occurred to Fleur to do that - she doesn't ever come off as vindictive, just aloof.
You can also see the Gryffindor primary when something happens that directly impacts friction that she feels with people. Fleur is absolutely implacable when she believes that someone is wrong, but she will make a very quick about-face if the conflict disappears. It seems pretty clear that she thought Harry had put his name into the goblet for glory in the beginning of GoF; when he saves her sister, it's clear that glory isn't what he was looking for, and Fleur suddenly becomes quite friendly with him. Even if she didn't know it in the moment, she had to have figured out later that Gabrielle wasn't in any danger; that didn't diminish her affection for Harry, because it was the principle of the thing and he'd done the Right thing. Similarly, she and Molly had had significant friction for a year; that friction pretty much vanished as soon as Molly stopped being Wrong about how genuine Fleur's feelings for Bill were.
In English Lessons, I definitely lean into that. She's clearly impressed by Bill being "a hero" - she uses that specific term multiple times, and it's clearly a priority for her. In the weeks leading up to their actually getting involved, she shrugs off his frequent cancellations and rescheduling of their English lessons because she (correctly) assumes that it's because of the war, and when he has the "so I'm not necessarily a safe person to get this involved with" a few weeks in, she surprises him by basically saying, "Well, if you're that involved in the fight, you're very brave, and I like that." (Paraphrased, because the language she uses is M-rated. ) And, in the fourth (currently WIP) one-shot, Bill asks Fleur why she's getting involved in the SWW. After a short back-and-forth, she says, "I do not think that wars belong to anyone. The wrong thing is the wrong thing. Here is a place where the wrong thing is happening, and here is a place where I can help, because I know you. That is why."
So: Gryffindor primary.
Secondary (the “how”)
Sidenote!Fleur is a Ravenclaw secondary (M):
Ravenclaw Secondaries plan. They collect information, they strategize. They have tools. They run hypotheticals and try to plan ahead for things that might come up. They build things that they can use later. They feel less at home in improvisation and more comfortable planning ahead and taking the time to be prepared.
I think it's strongly implied in canon that Fleur excels when she can plan. I honestly think that there was some sexism in how the first task was judged - Krum came in first despite having half of his eggs crushed, where Fleur was able to put a full-grown dragon to sleep all by herself without being injured - Ron didn't even leave an injury out, because Harry specifically mentions Cedric's burn. We saw 7-8 wizards struggling to stun one dragon the chapter before; are you seriously telling me that Fleur's skirt catching on fire and her extinguishing it quickly is worth docking her more than 10 points?? (Since Harry ended up with 50 and was tied for first with Krum, Fleur had to have lost more points than he did.)
At any rate: I think that that displays exactly the sort of thing Ravenclaws are known for. She's clearly good at dueling; she and Bill survived the Battle Over Little Whinging without getting injured, and Bill specifically says that there were half a dozen death eaters coming after the two of them and that Voldemort was close enough that they saw him kill Moody. She also survived the Battle of Hogwarts. We don't see Fleur in action very much, but if you read between the lines, she's good at it when she was able to prepare for the possible scenarios.
The one place where we see her genuinely fail is in the second task - and I would argue that that's the situation we know of her encountering that was the most difficult to truly prepare for. Being underwater is a completely different dynamic, and there were elements that she just couldn't have predicted or expected. An improvisational secondary (i.e., Gryffindor/Slytherin) probably would have managed it anyway (and, indeed, we see Harry pull it off). Fleur did not.
In English Lessons, Fleur's how hasn't quite come up yet in the way it will in a few chapters, but let me just put it this way: if you put a Ravenclaw secondary, a Gryffindor secondary, and a Slytherin secondary at a table, they can come up with some really interesting modifications to spells and some really reckless ways to keep them from falling into enemy hands.
In summary: Sidenote!Fleur is a Gryffindor primary and a Ravenclaw secondary.
(Italicized sorting-related quotes from sortinghatchats)