Hello Ratwitch! I've dabbled in genealogy in the past and can offer a little bit of advice. First get as many names as you can, your father's brothers, sisters, parents', grandparents, etc. Go to the Winnsboro town website,
Welcome to the Offical Web Site for Winnsboro Louisiana - Our Home on the Internet!, and get the phone number to the courthouse to see if you can get any records with your family's names. Use the town website to request info (information) on any local genealogy groups, and find the library address and/or phone number. Sometimes libraries have lots of information on local genealogy.
If your father was Catholic you could try contacting the Archdiocese to obtain birth and marriage records. Here's the site for the one in New Orleans,
Archdiocese of New Orleans, ask them who to contact for records in the Winnsboro area.
Another good source for information is the US Census for 1930, unfortunately the one for 1940, has not been released. I used to use this site a lot, ancestry.com, I paid a fee, but it saved me lots of trips to the library downtown.
I hope this helps a bit
. Best wishes!