Honestly, I've seen a ton of different directions taken with Henry/Elie pairings over the years. The most common one by far is just straight-up 'missing moments' during the Toppat Clan arc, where authors fill in the gaps between 'Infiltrating the Airship' and 'Completing the Mission.' They'll write about their dynamic as partners-in-crime, that slow build of trust, maybe a shared moment looking out over the airship deck. Some really dig into Elie being the more strategic, calm one to Henry's chaotic energy, which I think fits.
Then you've got the massive AU scene. Modern AUs are huge—coffee shop, college, office settings—where Henry is still a lovable disaster and Elie is the competent one who inexplicably puts up with him. There's also a surprising amount of soulmate AUs or fantasy crossovers. I remember one where they were rival thieves in a steampunk setting that was actually pretty well-written. The 'canon-divergence' where Henry chooses to stay with the Toppats with Elie at the end gets a lot of play, too, exploring what their life as leaders would actually look like.
My personal favorite, though, are the quieter post-canon stories that aren't just fluff. Ones that deal with the aftermath of all that chaos, the weirdness of settling into a 'normal' criminal empire routine, the unspoken things between them after everything they've been through. Those feel the most genuine to me.