On the one hand, he was extremely dedicated to achieving unconditional surrender. On the other hand, he was more willing to work with Stalin (afaik) than Truman, and Byrnes would never have become Secretary of State. Would FDR living to the end of WW2 have changed the outcome of the war with Japan?
Considering absolutely no one involved in the decision to drop the nukes actually thought it was necessary to do so, and FDR was a generally more reasonable person, I'd say he probably wouldn't have.