I checked the Social Security Death Index at Ancestry.com and found (1) Aaron Fuselier, born 29 April 1918, SS # ISS LA 438-16-0780; he died February 1981 in Eunice, St. Landry Parish, LA 70535.
When you find his death information on the SSDI, click on Write Letter and download a form letter addressed to the Social Security Administration. Submit the letter and $7 to the SS Adm. I am told you can receive a great deal of information from his SS application that should include the names of his parents.
Since you believe he was born in Ville Platte, Evangeline Parish, LA I suggest you write J. Wendel Fusilier Law Corp., 305 W. Magnolia, Ville Platte, LA 70586. Phone: 1-318-363-6661.
The Fuselier/Fusilier families have always been prominent in business and politics in and around Evangeline Parish.
Once you have found your great-grandparents' names, you should be able to find the remainder of your ancestors in Southwest Louisiana Church & Civil Records by Rev. Donald J. Hebert, Hebert Publications, P. O. Box 147, Rayne, LA 70578. SWLR contains 41 volumes, beginning with the year 1750 and ending with the year 1909.
The Evangeline Genealogical & Historical Society has purchased complete sets of Fr. Hebert's SWLR for every branch library in Evangeline Parish. The library in Birmingham, AL has the records and you may find these volumes in the library where you live.
I am a native of Ville Platte and have lived in Birmingham since my marriage in 1954. I still have family in Ville Platte and visit often.