Torches burn

Exposed as a baby and picked up by Agelaos, Paris is raised by him and his wife until he's sixteen. That's when he's discovered and subsequently taken back in by his biological family. After all, if he survived the exposure, being nursed by a bear, perhaps the (interpretation of the) dream was wrong? Perhaps he’s just meant to live. Guilty parents, either way, welcome him back. Paris lives a number of years in Troy until one early spring afternoon on Mount Ida shortly after his 20th birthday. He's herding some of the royal livestock when he's confronted with three goddesses, a god, and a golden apple.
He judges as he sees fit, and this sets off a whole, terrible, chain of events that will unfortunately prove that a stray torch will indeed burn down the city it’s been set to warm with light.

-His parents named their baby Alexander prior to giving him away to be exposed. He was also given a pendant where that name was scratched in on the back, which is how he gets recognized later. Agelaos and his wife named their new baby Paris, since they can't read.

-Paris still spends some time on Mount Ida herding the royal cattle after being rediscovered. He finds he still likes the task (even more so now compared to when he was a slave when it comes with more privilege and resources), as this is a perfectly fine occupation for princes. This leads both to a relationship (though not marriage) with the nymph Oenone for a little while shortly before he goes to Sparta and the chance to pit his pet/prize bull against others and, finally, against a disguised Ares, as he'd promised a golden crown as a prize if his own bull could be defeated.

-He's also (been) in love with Antheus, a son of Antenor, competing with Deiphobus for his affection**.

-A comment below has a longer treatment of what I consider canon for the Judgement. For a quick accounting, he has told almost no one he was offered a gift by each goddess, and he didn't ask them to undress.

-Aphrodite helped him overcome Helen's compunctions about eloping, since that's a lot more commitment than just banging while the husband's out. Paris was perfectly capable of seducing her on his own.
(I can be flexible about how this exactly went down and how much agency/willing Helen was, but I'm not interested in "there was no genuine desire/emotion there at all, it was all Aphrodite" nor "he straight up kidnapped and raped her and has been doing so for the length of the war, no matter how gentle he is about it".)

-By the last year of the war, he can be anywhere from 30-35; 30 if strictly the ten years of the war has passed, up to 35 if additional years are inserted between Helen leaving Sparta and the second muster at Aulis/the Achaeans arriving at Troy, as I usually default around ~5 years. Either way he goes to Sparta at 20.
(Pseudo-Apollodorus' Bibliotheke inserts 10 additional years, to match what Helen says in the Iliad about it having been twenty years since she left Sparta, for example.)

-As per the Epic Cycle fragments for the Little Iliad, Paris dies on the battlefield to Philoctetes during a duel. His corpse outraged by Menelaus but won back and buried.

Extra notes and variations

If you're interested in a version where Paris rejoins his birth family at ten instead of as a teenager, or one where he's grown up in Troy entirely (hewing even closer to what might have been the situation in the Iliad), excising the exposure entirely, if not the dream omen necessarily, then check more here.
**Technically this draws from a variation, referenced in Lycophron's Alexandra, where Paris accidentally kills Antheus (while playing discus) and has to go into the usual exile after such events, and goes with Menelaus back to Sparta after the latter has spent some time in Troy (hosted by Paris, even) for sacrifices at a couple tombs to lift an epidemic and curse of sterility on Sparta.
Obviously at least the latter part of this replaces any other version of how Paris goes to Sparta if not the Judgement itself (as that could still have happened), but the interesting parts are anything before Menelaus goes home with Paris along. If using the particular bit about the accidental killing, of course no exile would've happened and Paris was pretty damn distraught and inconsolable over what happened.

Shipping Corollary

Shipping in general: I would kill for Menelaus, any way, any how I might get it. Helen as well! Background/assumed OT3 in various AUs or canon divergences with either of these two would be loved!

Any other male characters welcome as well - especially Ares, jumping off from the bull fighting myth (and maybe Paris' possible similarities to Aphrodite?). I would not be averse towards Hektor/Paris, either (though platonic-only would be loved as well!).
Some vague exceptions aside from Helen only when it comes to f/m for Paris: eidolon!Helen for a darker flavour + femdom, Oenone is a maybe, please talk to me first. And again, femdom is pretty much a given for the dynamic, both in and out of actual smut, that I'm looking for.

Desires for Helen specifically: femdom vibes or outright that dynamic, both inside and outside of sex; I just prefer Helen as the dominant personality between them. It's not necessary if that's not what you jive with, but it'd be a very nice bonus, whatever else we make of their relationship.
Additionally, I am perfectly fine with (and would actually prefer) at least some acknowledgement of Helen being angry/disenchanted with him later in the war - as long as it's a "it's complicated" sort of thing, not straight up, all the time negative.

Canon-wise, I'd be really interested in exploring those days in Sparta before/up to Menelaus' leaves, but anything up to his death is welcome, as is post-death reconciliation in Elysium! Or post-Trojan war OT3 AUs, as well as no-war OT3 AUs. Various reincarnation verses definitely welcome, and for more straight up AUs, I'd really love omegaverse with alpha!Helen and omega!Paris.

Desires for Menelaus specifically: like mentioned above, any way I could get it. Playing out those nine days before Menelaus leaves, either as merely UST or a full-blown, developed mutual thing; tension of love-hate etc during the war as they meet in non-combat circumstances, or canon divergences to take the war in a different direction.
There's a rare variant where Menelaus goes to Troy first, needing to sacrifice at a couple tombs; I'd love to play that out, with a same sort of either UST only or developing into a fully realized mutual thing as above. Various AUs in general.

(As an aside, slightly different but vaguely connected to omegaverse AUs (up to and including Paris starting out as a non-typical alpha or beta and being turned into an omega), if anyone knows of D/s or BDSM AUs, that's definitely something I'd be interested in playing out as well.)

Various AUs

Reincarnation AU: A too large family (he's one of eight children) where Alexander has never been half again as interested in sports as all the other sons, where both his bisexuality, general interests, and behaviour induces mostly confusion from the rest of his siblings and most particularly his parents. One can only stand so much, and so Alexander has fled from their home in Mytilene, Lesbos (to where the earlier family members had come as survivors after the Greek genocide and the population exchange between Greece and Turkey; they're Anatolian Greeks with some Turkish ancestry), taking refuge in the larger population of Athens and the greater possibility of queer life there, attending theatre studies at the University of Athens.

Never mind all these strange dreams, but he figures reading the Iliad repeatedly since he was old enough to understand the language used has left strange marks.
-His first kiss was with a siren while on a boat trip; she would have sunk the boat if he hadn't unintentionally charmed her, not knowing what she was. His second kiss, a couple months later, was with the son of a tourist couple he met on a beach. Both of these were revelations in their own way.

(If set after his education, his parents got a little better about some things and, thanks to their wealth, he's able to worry less about work and can focus on theatre and music. Technically a minor celebrity thanks to his family, but also, lately, by his own artistic skill. By this point is reluctantly but irrevocably aware of, if not fully reconciled with his first life.
His full name is Alexandros Kasdaglis, (with his mother often using Alekos, he is pretty fond of that one). At some early point he picked up 'Paris' as a nickname, both among friends and some of his siblings.

Modern day vampire AU: Paris is shot by the arrow poisoned by the hydra gall, Oenone refuses to heal him - and Aphrodite swoops in to pick up her favourite once again. But she cannot heal him, really. She can only save him, even when saving means emptying him of the poisoned blood while using ambrosia to keep him alive, and feed him the blood of another to replace what has been lost.

Paris is probably not the first vampire ever at that point, but he's certainly the only one made by a goddess. Though he has lost so very much by the time he can move under his own power after the changes has worked through his body, he's still grateful to be alive. Even when learning what it means to keep himself such. Death does not beckon, and Alexander of Troy turns his face in the opposite direction, towards the future, and lives.

(Can certainly be combined with reincarnation AUs for other characters.)

-He's not the sort of vampire vulnerable to sunlight or faith*, but he does need to consume blood, and might even have low-key need for sex, too, but that's never been something he's had to figure out. He can otherwise be killed by regular means, but as he's more durable than a regular mortal, the most reliable method would be beheading.
-Paris' natural charm has now basically become a power. It might not be hypnotizing as such, but it's in the neighbourhood of that.
-It feels really good to have sex with him, aside from that he's great at it. Unlikely his partner is going to notice they're being fed from. Especially so if/when combined with the charm power.
*The exception is hubristic behaviour towards or denial of Aphrodite, as closely tied to her as he is.

Sad ghost AU: basically just means Paris haunts the ruins of Troy, resisting (so far) any attempt to make him leave for the Underworld. It's not as if anyone really wants him in Elysium anyway, right.

Underworld/Elysium: post-death, post-canon, Underworld setting for family reunions, running into (former) enemies, etc and so on. Can obviously be folded into Hades game canon.