Short of finding a definitive statement from Hardy, it is impossible to be sure. But it is very likely that A Few Crusted Characters was influenced by The Canterbury Tales.
I have three lines of evidence. First, we know that Hardy was familiar with The Canterbury Tales. Here's JoAnna Stephens Mink, in "Love, deception, and disguise in A Few Crusted Characters":
Hardy's careful structure of Crusted Characters has literary precursors, but he subverts the convention of Boccaccio's Decameron and Chaucer's The Canterbury Tales, with which his London readers would have been familiar. Several parallels suggest that Hardy had these literary masterpieces in mind when organizing Crusted Characters. In fact, only three years before writing the stories, he included "Boccaccio / Canty Tales" on the list of "Books read or pieces looked at this year" in his note for December 31, 1887.
(For the claim in the last sentence, Mink cites Florence Emily Hardy (1933), The Life of Thomas Hardy: Compiled Largely from Contemporary Notes, Letters, Diaries, and Biographical Memoranda, as Well as from Oral Information in Conversations Extending Over Many Years.)
Second, contemporary reviewers took it for granted that the structure of A Few Crusted Characters was inspired by Chaucer. For example, a reviewer in The Literary Era (1894) wrote:
what are we to say of the colloquial sketches, entitled "A Few Crusted Characters," which form the latter portion of the book? Here on the van of "Burthen, Carrier to Longpuddle," we meet a party of country folk, and everyone tells a story after the manner of the Canterbury tales
Third, The Canterbury Tales is one of the best-known works in English literature. The British Library notes that it was "enormously popular in medieval England, with over 90 copies in existence from the 1500s". It has inspired many works over the centuries, including:
The narrative framework in which a group of storytellers each tell their tale is not, of course, original to the Canterbury Tales. Chaucer himself was influenced by Boccaccio's The Decameron (1353), and Boccaccio by John of Capua's Directorium Vitae Humanae, a translation of Ibn al-Muqaffa's Kalīlah wa Dimnah, itself ultimately a translation of the Sanskrit Panchatantra. Nonetheless, Chaucer remains the most well-known model for this kind of frame narrative in English.