Michael, these are the only local records I could find on this family. Hope they help you put together a few pieces of the puzzle.
Records in Terrebonne/Lafourche reference books for surname Fluence or varient.
South
LA Records by Donald
Hebertvol. 9 p. 214
Fluence, Maria m. 6 June 1892 Joseph
Jefferson (Thib Ct Hse Mar v. 32 #145)
vol. 10 p. 216
Fluence, Oscar m. 6 March 1897
Ophelia Davis (Houma Ct Hse Mar v. 29 & 30, #338)
Fluence, Willie m. 25 March 1896 Mary
Parker (Houma Ct Hse Mar v. 31 & 32, #64)
Flunce, Charlie m. 1 July 1899 Anna
Robertson (Houma Ct Hse Mar v. 31 & 32, #64) (no typos)
v. 12 p. 38
Fluence,
Willis m. Lucinda Fluence Child listed: Frederick, oath of under-curator: 16 Jan 1911. (Thib Ct Hse Succ #1600)
_________________________________________________________
South
LA Vital Family
Records by
Terrebonne Genealogical Society
vol. 1 p. 68
Fluens,
Willis "Gardianship" of his minors (Hma,
LA Ct Hse Succ #997 1/2, filed 4 Feb 1903
vol. 3 p. 96
Fluent, Armie, 25 (Sandy Fluent) m. Olivier Johnson 17 Nov 1913,
Lafourche minister (Thib Ct Hse Mar v. 1913, Lic #215)
vol. 4 p. 95
Fluence, Agnes age 20 (Wm. &
Cecile Turner) m. Johnny
Jones 22 Feb 1917 minister (Thib Ct Hse yr 1917, Lic #66)
cross ref for Johnny
Jones page 135 - age 21 s/o Willie
Jones and Caroline
ParkerFluence, Mabel (Oscar and
Ophelia Fluence) m. Christopher
Collins 1 Jun 1916 Beattieville (Hma Ct Hse v. 49, p. 296)
cross ref for Christopher
Collins page 65, s/o Mose
Collins and
Sophie Wallace
Flurence,
Lucinda Mrs. d. 20 Apr 1917
Lafourche Parish w/o Willie Flurence
vol. 5 p. 87
Fleurence,
Lucinda Mrs. d. 20 Apr 1917, w/o
Willis Flurence (Thib Ct Hse Succ #2359, filed 28 March 1819)
Florence, Lillie age 22 (Oscar and deceased
Ophelia Davis) m. Peter S. Tibbs 27 Oct 1920 minister (Thib Ct Hse yr 1920, Lic #329)
cross reference for Peter S. Tibbs page 220, age 40 of M.C. "widr. of Mary Jane Finney" (deceased Samuel
Tibbs and deceased Eliza Rassnolit)
Fluence,
Ophelia d. 1 Dec 1918, bur Mt. Olive Bapt. Ch.
vol. 6 p. 80
Fluence, Annie (Oscar &
Ophelia Davis) m. Gillis George, 29 Sep 1921, Beattieville minister (Houma Ct Hse v. 54, #391)
cross ref page 87 for Gillis George (
Neuville George & Eliza
Robertson)
Fluence, Femelia (Will & Mary Fluence) m. James Woodbery Jr., 15 June 1922, Gray,
LA, minister (Hma Ct Hse v. 55, #305)
cross ref page 220 for James Woodbery Jr. (James Woodbery Sr. and Mary
Stevens)
No further records. Books stop at 1941