It's safe to say that the Trojan War as told by Homer (or whoever really told the story) didn't actually happen, but it's quite possible that the tale has some truth to it; an amalgamation of various oral stories that had been passed down again and again, becoming more fanciful over time.

If the Trojan War has any basis in real battles, the most likely candidate is called "Troy VII", which is just one of the layers of a site in Anatolia, "Hisarlik" - which is mostly thought to be the most likely candidate for a historical Troy - that was built on many different times over. There's two layers that roughly correspond to the purported period of the Trojan War: Troy VI, destroyed by an earthquake around 1275 BC, and Troy VII, which is believed to have been built on the ruins of Troy VII by the earthquake's survivors.

Troy VII shows evidence of being subjected to siege, capture, and destruction (by fire) during the general period that Greek tradition purports the Trojan War to have occurred.

However, overinterpretation of evidence is pretty rife when it comes to searching for Troy/the Trojan War, so this should be taken as a mere possibility rather than definitive proof of anything.

Outside of archaeological evidence, the Iliad makes references to pre-Homeric stories, which indicates that the characters might have been something of an established beforehand, and perhaps there were lost stories involving them dating back who knows how long. Achilles is also an authentic name that is roughly contemporary to the time period of the Trojan War. Yet there's no known historical figures who the characters might be based on, so take that with a grain of salt; it just shows that there might have been some sort of story of a dude named Achilles/etc that was heavily diluted/added to over the centuries until he somehow became the superhero we're familiar with.

Does this answer the question? No, not really. It's not something that will ever be definitively answered, especially since it's pretty much impossible there's some jackpot written source hiding somewhere; writing only became commonplace among Greeks about 500 years after the purported fall of Troy, and by that time anything that had been passed down orally was doubtlessly heavily diluted. But it's possible that it was actually based on something, though I wouldn't bet on it being anything near as grand as what The Iliad tells us.