I too have long been contemplating a Frieren build. The ideas I've come up with...
Ancestry
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Elf obviously. Seer Elf makes the most sense for heritage since it grants detect magic as an innate spell and grants a bonus to identify magic, something Frieren proves adept at in the source material.
Her initial ancestry feat would be a toss-up between Ancestral Longevity and Forlorn. I ultimately favor Forlorn since Frieren's gradual emotional processing of the mortality of her friends is central to her character, and while she's well learned from her experiences her skill-set has been fairly consistent and nothing unexpected so mechanically it felt harder to justify Ancestral Longevity.
Class
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Definitively Wizard, learning magic is Frieren's favorite thing to do! The Arcane Thesis is tricky and there's not really a right or wrong answer here. The only Thesis I'd rule out is Improved Familiar Attunement since Frieren does not appear to rely on a familiar at all in the series. All the others could apply to Frieren quite well given what the series has demonstrated.
Arcane School on the other hand would easily be School of Unified Magical Theory; Frieren loves magic and would like to keep her studies broad. Plus in her home series she is apathetic to the numerous organizations that have tried to regulate magic she has seen come and go in her long lifetime.
Skills
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She'll obviously focus on Arcana. I also picture that she'd like Crafting to satisfy her fascination with odd doodads and bobbles. Given that much of her early training was about learning how to fight and deceive demons, getting additional Lore for Demon Lore would also make sense (or whatever fits your setting; Frieren Demons are a different beast from Pathfinder Demons). Some considerations for tertiary skills would be Acrobatics or Stealth given we've seen her maneuver across rugged terrain or in flight, and there's also the fact that ambushes would be completely within her combat philosophy (though her student, Fern, has demonstrated greater proficiency in hiding than Frieren).
Class Feat suggestions
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Counterspell and eventually Clever Counterspell: Frieren has proven quite adept at analyzing and counteracting magic in her home series - see Aura's puppetry spell and Serie's barrier.
Cantrip Expansion and Bond Conservation: She likes magic, even the silly little spells, and these give her more spells to use in a day.
Spell Mastery: I mean there's an argument for other 20th level class feats, but I feel Spell Mastery best captures a Frieren-like build. Frieren's usual combat philosophy in her home series is to stick to basic spells when those will do the job, which suggests that she doesn't prize super powerful or complicated spells any more than she would other spells; plus this also just generally gives her more spells to cast in a day.
This is all just speculation of course but I think the above points can emulate Frieren as best as possible in this system.