Hi Judy Gallant-Root,
Indexed entry for marriage of Francis Henry Pigeon (Pigeon-50) and Mary Appollin Labrigue is reported in the FamilySearch Collection, "Rhode Island Marriages, 1724-1916."
"Rhode Island, Marriages, 1724-1916," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/F8KK-H2S : accessed 21 Jul 2014), Francis Henry Pigeon and Mary Appollin Labrigue, 08 Oct 1876; citing Burrillville,Providence,Rhode Island, reference ; FHL microfilm 941604.
The Family History Library film cited is [Burrillville (Rhode Island). Town Clerk,] "Town meeting records, 1806-1881." Using the information in the citation, you should be able to order a copy of the record from FamilySearch's Photoduplication Service.
The indexed record, linked above, calls out both the bride and groom's parents names.
P.S. Birth record of Esther Pigeon, b. 01 Jul 1880 at Leicester, Massachusetts, reports her parents as Frank Pigeon and Mary Labreque--both of whom are there reported born at Canada.
"Massachusetts, Births, 1841-1915," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/FX7G-SPM : accessed 21 Jul 2014), Frank Pigeon in entry for Esther Pigeon, 01 Jul 1880; citing Leicester, Massachusetts, 298, Massachusetts Archives, Boston; FHL microfilm 1428202.