Without going too much into that... stupidly elaborate backstory for that character of mine, he'd be a LOT, and I mean a whole lot, more involved with the whole Dragonsong War, even as soon as when Alphinaud, Cid and he come to the Central Highlands - he is a Coerthan-born-and-raised person after all.
That, and generally a lot more tackling people to the ground in overbearing affection. Or plain tackling them to the ground because he feels like it. Or putting live snakes in Estinien's armour in early Heavensward (someone has to prove their dominance as Azure Dragoon, and he's gonna do so by snakes and chocobo feces, the Fury be damned).

Okay, joking aside, he'd... actually follow the canon plot of the game a lot, he is Lawful Stupid until 3.0 ends. Anyhting following that would be slightly more him on edge and ready to punch and/or maul people (Thancred shouldn't be the only one getting to punch Emmanellain across his face PLEASE)