This one might depend on whether Perot jumps back in or not after dropping out. Assuming Perot doesn't, I think Campbell would do much better in the South than Bush did, basically winning everything except Arkansas (and maybe Tennessee, assuming Clinton still picks Gore in this universe).
It still isn't enough to win, and Perot being off the ballot means Clinton does slightly better in the popular vote, as more Perot voters outside of the South go to him over Campbell.
Governor Bill Clinton (D-AR)/Senator Al Gore (D-TN) 50%
Governor Carroll Campbell (R-SC)/Senator Trent Lott (R-MS) 46%