Wartime dropping the bomb is an inevitability when one has three weapons and uses one for a test, one does not waste 50% of your stockpile on a demonstration to the enemy.
Domestically, we'd see him push a legislative program similar to Truman's Fair Deal and his own Second Bill of Rights. His ability to pass such a program being something that one can debate for hours on end, though I'd say that winning the Second World War will give him some credibility that he'd lost back with the Court-Pack Game.
Internationally, well, to be nice, see Henry Wallace in 1948 for that. With awful heaping of trying to aid the KMT in China beyond all reason. One can't expect free elections in Poland or Czechoslovakia just because he's still in charge.
With the greatest Democratic President of all time alive in 1948, but with his power really at an end, the national convention still has a good chance of breaking in three as per IOTL. Truman's time will have passed and he'll probably either retire or try to go back to the Senate.
If FDR is able to keep his wits and political savvy about him until the end he'll try and pick a successor who would be acceptable to as many factions of the party as possible. Truman would be out, it wouldn't be a Southerner, nor could it be Wallace no matter how much FDR might like him for continuing his foreign policy. Most of the 1940 possible heirs have waned in the 8 years that followed. So possible heirs FDR Might propose would be Secretary James Forrestall (My personal pick, though it probably goes badly), General of the Army George Marshall, Senator Scott W. Lucas or Alben W. Barkley. Though none of those can be assured to prevent at least one of the two break-aways of OTL to do so here.