Found no Paul or Parks in 1870 Census Index (AIS).
1. Found the following (selected) in 1870 LA Index:
- Aaron 31MB NC (E. Baton Rouge), 2 Ward, Baton Rouge (PO), p. 81
- Solomon 65MB NC (Assumption) Napoleonville PO p171
- Joseph 40MB MD (Assumption) Napoleonville PO p188
- James 35MB VA (Lafourche) Thibodaux PO p493 [Living alone]
- J.(initial only) 36MB LA (St. James) Cantrell PO p. 250?
- Hampton 60MB NC (Assumption) Napoleonville PO p180
BARNS, Phill 30MB LA (Ascension) Donaldsonville PO p55
BERNARD (no Sarah, but the index is only HOH)
- Celestin 26 m b LA Assumption Napoleonville PO, p291
- Mary 17 f b LA Terrebonne Houma PO p. 371
- Patsy 30 fb LA Ascension Donaldsonville PO, p. 35
- Rosalie 75 f b LA Lafourche Thibodaux PO, pg. 394
2. Found the following in the 1890 Special Census of Civil War Vets
BARNES, Edith* (Assumption) Bruly Dalferes
*wid of Salaman Barnes per Terrebonne Life Lines Vol 13, #3, page 66
[Terrebonne Genealogical Society, article: "1890 Census Assumption, LA Civil War Vets" ]
BARNES, Emile (Assumption) Bruly Dalferes, ED60
BARNES, John (Lafourche)Thibodaux
BERNARD, Celestin* (Assumption parish) Bruly Dalf
*U.S. Pvt 84th US Col Inf 1862-1865 (served 3 years) [per TLL Vol 13 #3]
BERNARD, Augustus -Assumption, Bruly Dalferes ED60
3. Diocese of Baton Rouge Catholic Church Records, Vol. 18 1889-1891
Joseph BARNES (Park and Sarah BERNARD) bn 17 Sept 1890 bt. 14 Mar 1891 Sponsers: Lee VINCENT & Marie TURNER [SPH-10,9 - St. Philomena Church, Labadieville,Assumption, LA]
BTW: Labadieville is about 5 miles from the Lafourche parish line, and 9 miles from Thibodaux Town center. Donaldsonville is about 30 miles up the bayou (Lafourche).
4. *Barnes, Walter m. Elizabeth KYLE (p: V. H. KYLE) at St. Matthews Church on 6/03/1923; Paper dated: 6/9/1923 [No indication if this is your BARNES family, however.]
* Per TLL, Vol. 12 #1, pg. 60
Found another record in the Diocese of Baton Rouge church records, Vol. 18:
Walter BARNES (Drauzin and Easter BARNES) bn 30 Nov 1890 bt. 7 Mar 1891 Spo. Telexlo Toussaint and Emma MACK (SPH-10,9) St. Philomena Church, Labadieville, LA [Also no indication if this is the same Walter or your BARNES family. Just thought I'd throw it in for good measure.]
5. BARNS, John d. 30 Aug 1901 at 66 yrs Old (Thibodaux Church), per "South Louisiana..." Records by Rev. Donald J. Hebert. [Hebert Pubs]
I ran out of time at this point. Terrebonne Genealogical Society has published the vital records of Lafourche and Terrebonne in book form. They also publish (some) original records of Assumption parish, as well as cemetery records...(see link).