The census data is a long shot, however, you might try the County Clerk in Bexar, TX to see if there is a death certificate you can obtain that might have more information.
U S Census, 1940 Fenton, Police Jury Ward 5, Jefferson Davis, LA
Citing this Record: "United States Census, 1940," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/VYP9-3V9 ), I J Norman Fontenot in household of Ransy Fontenot, Fenton, Police Jury Ward 5, Jefferson Davis, Louisiana, United States; citing enumeration district (ED) 27-13, sheet 19A, family 327, NARA digital publication of T627, roll 1408
Census Image: https://familysearch.org/pal:/MM9.3.1/TH-1942-27770-482-30?cc=2000219 Note: This census page has multiple Fontenot families.
Ransy Fontenot Head M 34 Louisiana
Tressie Fontenot Wife F 31 Louisiana
I J Norman Fontenot Son M 11 Louisiana ???
Elaine Fontenot Daughter F 8 Louisiana
Erma Fontenot Daughter F 4 Louisiana
Shelton Fontenot Son M 2 Louisiana
United States Public Records, 1970-2009
Citing this Record: "United States Public Records, 1970-2009," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/KPG5-PZ9), Linton J Fontenot, Residence, San Antonio, Texas, United States; from a third party aggregator of publicly available information.
Name: Linton J Fontenot
Residence Date: 01 Jan 1998-13 Jul 2001
Residence Place: San Antonio, Texas, United States
Birth Date: 28 Sep 1928
Phone Number: (210) 655-7171 Recorded Date: 01 Jan 2004
Address: 902 Impala San Antonio, Texas 78258
Address Date: 01 Jan 1998-13 Jul 2001
2nd Address: 5842 Moores Crk San Antonio, Texas 78233
2nd Address Date: 01 Jan 1994-01 Jan 2004
3rd Address: 5842 Moorecreer San Antonio, Texas 78219
3rd Address Date: 01 Jan 1967-01 Dec 1993
Possible Relatives: Hedwig S Fontenot
Record Number: 72678309
Texas, Death Index, 1964-1998
Citing this Record: "Texas, Death Index, 1964-1998," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/JVKC-QZ3), Linton Joseph Fontenot, 28 Sep 1991; citing Bexar, Texas, United States, Department of State Health Services, Austin.
Name: Linton Joseph Fontenot Male
Death Date: 28 Sep 1991 County: Bexar
Place: Bexar, Texas, United States