Hmm. My first thought was to look at Louisiana, as I hypothesized Smith may have received a Catholic boost that FDR didn't get in Cajun Country.
I see that Iberville Parish voted 85% Smith, but only 75% FDR. Iberia is 86% Smith and 75% FDR. St. John the Baptist is 89% Smith and 80% FDR. St. James is 92% Smith and 88% FDR.
It looks like there are more, but because the swing/trend feature doesn't go back that far, checking is kind of time-consuming. If you have any ideas of where else to check, I would be happy to do so.
There are no swing/trend maps, but there is swing/trend data available on the data tables, which can be sorted by swing/trend.