The Actual Duration of the War
Towards the end of the Iliad, whose action takes place in the tenth and final year of the Trojan War, Helen says (in Line 765 of Book 24) that "this is now the twentieth year" since she departed from Lakedaimon [Lacedaemon] with Paris. "The words have puzzled the Scholiasts and commentators"1 for centuries because one might have expected the duration mentioned by her to be closer to the length of the war; but the war's length accounts for only half of the amount of time she's talking about.
Having been lost in ancient times, the portion of the work attributed to Apollodorus entitled the Epitome was discovered in 1891, and it contains a full explanation for this duration. For the Greeks the war had indeed lasted about twenty years. They had landed in Troas only nine years prior to the beginning of the Iliad and had engaged the Trojans immediately. However, they had first mustered up their forces to head for their enemy's territory in Asia eight years before their arrival in Troas.
Not really knowing their way there, combined with additional shenanigans that transpired, they landed in Mysia, mistakenly thinking that that was Troas, and eventually all ended up back home in Greece. They only managed to reassemble eight years after that debacle, which is narrated in Epitome 3.17-19ff. Prior to the first assembly, they had spent two years making preparations to build their army. So 2 years of prep + 8 years of reorientation & re-prep + 10 years of combat = Helen's 20 years as mentioned in the Iliad.
Akhilleus' [Achilles'] Age
Just before the chaos at the first gathering ensues, the Epitome tells us (3.16):
So Agamemnon in person was in command of the whole army, and Akhilleus
was admiral, being fifteen years old.
The Iliad mentions nothing so specific about the ages of Akhilleus and Paris, but the Epitome does inform us of how old Akhilleus is when the timeline is set at eight years before the beginning of the siege of Troy.
15 + 8 = 23. So Akhilleus is about twenty-three years old when the Greek army lands in Troas. Akhilleus dies in the last year of the war a decade later = about Age 33.
This also accounts for the pesky issue of the fact that Akhilleus' son Neoptolemos [Neoptolemus] arrives at Troy in the same year that the city falls, by then evidently a full-grown warrior of a man! If Neoptolemos was born in the same year of the first army gathering, or even the year after that (allowing that he could've been born in his father's absence), he would be roughly 17 or 18 years old when he helps to take Troy.
Like Akhilleus, Paris, when he was quite young, had a son. Paris's childhood sweetheart was a Naiad named Oinone [Oenone]. His intrigue with her does not receive mention in the Iliad, but other mythographers tell us that Paris was already married to Oinone when he met Helen, and even before he met Hera, Athena and Aphrodite.
The son of Paris and Oinone was called Korythos [Corythus], who, together with his mother, was abandoned by Paris when the Trojan prince left Asia in pursuit of Helen. After Paris had returned to Troy with the Lakedaimonian [Lacedaemonian] queen, as we know, the Greek army was eventually coming for him.
As observed above, this army did not enjoy immediate success finding its way to Troy. Oinone, perhaps because she was a prophetess (as in Apollodorus' Bibliotheka and Ovid's Heroides), was apparently aware of this since she sent Korythos to the Greeks to help them navigate (going by Lycophron's Alexandra 57 [via Tzetzes' commentary]).
In Conon's Narrations 23, Oinone sends Korythos to Helen, while in Parthenius' Erotika Pathemata 34, Korythos
came to Troy to help the Trojans, and there fell in love with Helen.
She indeed received him with the greatest warmth—he was of extreme
beauty—but his father discovered his aims and killed him.
By all accounts Korythos was at least a young man by the time of the war, and if we follow Lycophron on this, we was old enough to set out by himself to go meet a fleet of enemy ships and offer them directions which they, presumably, received well enough.
I would say that, reasonably, he should have been at least fifteen years old at that point. This would be, perhaps, roundabout the year before the siege of Troy begins. (I.e. Korythos guided the Greeks to Troy and they attacked in earnest when they landed the following year.) If we borrow the age calculations of Akhilleus from the breakdown above, let's say that Paris was also at least fifteen years old when he had Korythos.
15 + 15 = 30. Paris is (at least) thirty years old the year before the Greeks make landfall in Troas.
30 + 10 = 40. Paris dies at around the age of forty in the last year of the Trojan War.
There isn't much difference in the final result if Paris is 20 at the birth of Korythos and/or if Korythos is five years younger than in the preceding calculation (if we allow that Korythos can be younger in the versions of his story which don't involve him granting help to the Greek military). In the higher estimate, Paris would be about 35 at the beginning of the siege, and 45 at death.2
1. Footnote 4 on p. 187 of Apollodorus: The Library, with an English Translation, in Two Volumes by Sir James George Frazer. 1921. William Heinemann, London, & G.P. Putnam's Sons, New York
2. Assuming that Akhilleus was born in the same year as his parents' wedding; and allowing that Paris was about, say, eighteen when he adjudicated the beauty contest of the goddesses, this would mean that the goddesses had been squabbling for at least six years, between that inauspicious wedding and their fateful meeting with the Trojan prince. The calculations for this are as follows:
45 - 33 = 12. Paris is (at most) 12 years older than
Akhilleus (based on their ages at death).
18 - 12 = 6 years between the wedding of Peleus and Thetis & the Judgement of Paris.