A group of quarrelsome city-states united into a militaristic empire in order to take out another rival empire, that descends into centuries of warring with each other, only to be conquered by some jackasses in togas?
Greece and Rome work as broad analogues for Arlathan and Tevinter if you take the Macedonians to be the Evanuris. 
I actually had a somewhat similar thought after I posted that - if you consider each Evanuris (Evanura? Evanuri?) and their followers to have been their own city-state. Athens as the juggernaut of philosophy and culture that reflects Solas' (And likely Mythal's) view of Arlathan, but with other, more militaristic city-states like Mycenae and Sparta as parallels for Andruil, Falon'Din, etc. And Macedonia did expand all the way out to India. Didn't last very long, but they managed it.
I wish I could expand upon the idea more, but most of my knowledge of Greek history comes from Greek myth which is... not exactly a reliable historical record. That and it didn't seem like there was a whole lot of interest in the discussion.
I'm not entirely sure, but I think Varric makes some mention of a printing press, which would go a long way to explaining the books being everywhere. The other explanation is just that the writers want to give us lore and codex entries, and maybe goes a little overboard.
Thedas's level of technology definitely doesn't follow the Earth model, thanks to the presence of magic. The Qunari, having restricted themselves from using too much magic, have cannons and the beginnings of chemical warfare. China had these things for centuries before Europeans got their hands on them.
I'm in the camp of thinking that the Renaissance wasn't fueled entirely by the discovery of the classics. It certainly played a large role, but we can't discount the role of increasingly centralized states being willing to fund all this research, the eventual printing press's role. With juggernauts like Orlais, Nevarra, and Tevinter happy to shell out the coin to increase their prestige against their rivals, I can see there being an intellectual flowering in Thedas, likely further fueled by the dwarves getting their act together, the Qunari Wars of previous centuries showing what technology can do, and the usual competition.
Maybe. If knowledge and technology can be claimed from the Qunari and Dwarves (Which isn't impossible, given how there's almost certainly going to be a war with the Qunari at least.) But I doubt either would share their advancements willingly, since Dwarven culture makes extensive contact with surfacers difficult and the Qunari obviously aren't going to start handing their advantages over to the enemy.
But... writing this out has made me wonder something. I don't think we should be looking at technology as the.. heart (?) of a potential Thedosian Renaissance. It'll play an aspect, sure, and if we assume that period's already started, then it's probably progressing already. It's magical knowledge and progress that made past civilizations like Tevinter and Arlathan great. It's magical knowledge and progress that's currently being stunted and repressed by the setting's Christian Church expy. And it's magical knowledge and progress that Solas is trying to restore and advance. So I think, at least as far as parallels to the Renaissance go, magic will be far important than copies of our real-world technology.
And I know this is getting into that whole magic vs. technology debate from a while back, so I want to be clear that I'm not saying the technology's unimportant, or won't be advanced as well (Well, it probably won't if Solas murders everyone who knows anything about that stuff, but details, details.). I'm just saying that, if any sort of intellectual flowering takes place, magic and what can be done with it will be a much bigger factor than anything else.
...But all this talk of Solas' plot being a sort of parallel to the Renaissance just makes Orlais' Regency flair even more questionable. Before I was just willing to chalk it up to the writers' using a kitchen sink version of European history, now it seems more like they carefully crafted a Renaissance metaphor, only to have Orlais skip a few centuries into the 1700s.
*Sigh* Give me back your empresses and masquerade balls, Orlais, you'll get them back when you've suffered through three or four centuries of cultural revolution. And at least one possible apocalypse.