First we should establish what the "Age of Chaucer" is. Chaucer lived during the second half of the fourteenth century. His life spanned an extraordinarily tumultouous time in English and European history, one which witnessed the Black Death and the Hundred Years War. Chaucer himself served in the Hundred Years War.
More importantly, Chaucer represented a growing trend throughout Europe to write in the vernacular. At a time when most scholarly writing was done in Latin, and it was still a crime to translate the Bible into the vernacular, as John Wycliffe did during Chaucer's life, this was an important stylistic choice that connected Chaucer's work to a long tradition of vernacular poetry that included El Cid and The Song of Roland. It is known that Chaucer read, and translated a great deal of French poetry, and that he had also read the poetry of Dante, Petrarch, and Boccaccio, all of whom wrote extensively in the vernacular. Some of his poems explicitly draw from Italian themes. One of these themes is an interest in the secular (with the notable exception, to some extent, of Dante's most famous work.) Chaucer too portrays a world where actions have consequences, and people are driven to make choices by a combination of class influence and individual free will.
Yet religion played a powerful role in shaping the medieval worldview. His characters are, after all, on a religious pilgrimage. Just as important, Chaucer's characters reflect a hierarchical chain, and indeed his contemporary readers would have recognized the speech, manners and dress as stereotypical of the class to which each character belonged. The Canterbury Tales is best understood as a product of its own time, and religion and class were as important in shaping his work as the influence of other European poets.