He wouldn't run again. Supposedly he wanted to be the first leader of the United Nations after the war.
Presumably Truman and Dewey still are the nominees, and I bet Truman still wins. It's possible FDR might even step down early to go to the UN and let Truman take over after the war, meaning the situation probably wouldn't be too different except Truman would have FDR's active support behind him which could be an extra asset for him.
I don't think Truman would have been the nominee as sitting vice president. He was not a member of FDR's inner circle and probably wouldn't even seek the presidency himself. Maybe Eisenhower runs four years early and wins handily? Dewey becomes Attorney General in his cabinet then.
Not sure Roosevelt would have resigned around 1946 to become UN General Secretary. No president had ever resigned before at that time.
