It would be difficult to determine the exact year. The author, Geoffrey Chaucer, was born around 1343, and died, it would seem, in 1400. The Canterbury Tales, his mature masterpiece of English prose and rhyme, he likely wrote in his forties. That would probably place the year of composition sometime in the late 1380's. However, the exact year is not as important as Chaucer's wry and satirical portrayal of characters representing a cross-section of the religious and civil society of his time. Since the martyrdom of Archbishop Thomas a Becket 200 years before, pilgrims from every social class, and for every conceivable motive, had been making their way to Canterbury. Thus, in a sense, Chaucer's Tales could have been set in any year.
As to the time of year, it is early spring, as the poet tells us:
"Whan that Aprille with his shoures soote...and the yonge sonne/Hath in the Ram his halfe course y-ronne,...Than longen folk to goon pilgrimages,..."
As the earth regains its vitality, celebrated by the author in the first twenty lines of the poem, so people desire the adventure of a pilgrimage.