Hi Abby, sounds like a fascinating character. Net searches seem to turn up bits and pieces about his 1946 campaign, but no mention of the song. However, I found the following reference (if it can be tracked down) which may help if all else fails:

'THE STRAWBERRY PICKERS': "Big Jim" Folsom's 1946 campaign for Governor of Alabama -- the Music, the Politics and the People Involved, by Roy Baham, Jamelle Folsom and E. Jimmy Key. Nashville: Southern Arts, 217 pages, hardcover.

--Stewie.