Claire is the child of Altair and Vega and
Claire was teleported out of Vega's womb and into the womb of the woman who gave birth to her (and apparently died soon after)
are both true statements and bravely default canon(?)
Hold on, i knew the stuff in the main post, but i don't know this stuff in the tags
Can mew elaborate on this?
This is a bit difficult to explain but this is based on my understanding from both the "Reports"/Journals that are written from someone's POV during the events of the BDBL game and the cutscenes from the game itself.
The basic premise of the game is that Lumina needs to gather 8 crystal lifelines - 4 from Luxendarc (Default 1/Second) and 4 from Excillant (Default II) so the party spends 8 chapters gathering those up. This is because the worlds are destabilizing, and borders are getting erased, which is how people from both Luxendarc and Excillant end up in Vermelio. Eventually, they end up in each other's worlds - Bahamut from Luxendarc ends up being mistaken as the son of the Lord of Dragons in Excillant.
When they're finished, Lumina ends up with a crystal child/seed, a golden magatama looking thing.
(Also there's some plot about Vermelio being on the edge of war and other stuff happening but that's not important here.)
In Chapter 10 the big bad (Zarel, as mentioned in the screencap below) begins to lose control of the Crystal of Darkness inside them, which will destroy the world.
At this point Claire finds out she's Altair and Vega's daughter and contains her mother's wish to prevent the end of the world and stay with her loved ones. She uses the power of alchemy, being an alchemist, to create... something... that stops/seals Zarel's crystal but kills her.
So to bring Claire back to life, Lumina implants the Crystal Child/Seed within her. The below passage is from a subsequent report written from Claire's POV.
look okay i just want whatever they're smoking