There is very little to go on when assessing what FDR thought about the atomic bomb. He played his cards very close to his chest and he didn't keep any kind of written record on the subject. In general FDR does not leave much of a trail for historians when it comes to assessing his inner thoughts — it is just part of how he was.

So we have very few data-points by which to assess his views, and we have to do a lot of interpretation. FDR was certainly gung-ho about building the bomb — he was the one who authorized the project — but about using it, there are basically only two relevant things.

One is the memorandum of understanding that he developed with Churchill at Hyde Park in September 1944, which included the following:

The suggestion that the world should be informed regarding Tube Alloys, with a view to an international agreement regarding its control and use, is not accepted. The matter should continue to be regarded as of the utmost secrecy; but when a “bomb” is finally available, it might perhaps, after mature consideration, be used against the Japanese, who should be warned that this bombardment will be repeated until they surrender.

("Tube Alloys" was the British code-name for the atomic bomb.) So that implies that the idea of it being used against Japan was something he was thinking about with regards to the bomb, but it is worded rather hesistantly.

Second, we have an account from General Leslie Groves, head of the Manhattan Project, who many years later reported the following:

At the conference that Secretary Stimson and myself had with President Roosevelt shortly before his departure, I believe it was December 30th or 31st of 1944, President Roosevelt was quite disturbed over the Battle of the Bulge and he asked me at that time whether I could bomb Germany as well as Japan. The plan had always been to bomb Japan because we thought the war in Germany was pretty apt to be over in the first place and in the second place the Japanese building construction was much more easily damaged by a bomb of this character than that in Germany. I urged President Roosevelt that it would be very difficult for various reasons.

Which implies a willingness to use the bomb not only on Japan but even on Germany. But this was a moot question since they didn't have a bomb ready at the time.

That's more or less it. There are a couple other little places where the question of use came up, which I've written about at length here, but other than the above they are pretty remote in time from the actual possibility of it being used. Real planning to use the bomb only began in the Spring of 1945, shortly after Roosevelt's death. So he was never involved in any aspect of that.

Would Roosevelt have been different than Truman with respect to the bomb? Probably — but that doesn't mean he wouldn't have ordered it used. Truman was exceptionally "hands off" when it came to the atomic bomb, and was not actually very involved in discussions about its use (much less any "decision" to use it). Roosevelt was far better informed and far more used to playing a role in such decisions; I find it unlikely that he would have taken a back-seat to these things the way that Truman did. I suspect (and this is just an interpretation/guess) that he would have supporting using it on Japan; there were many reasons to use it apparent to people at the time, and very few reasons against using it. But I suspect some aspects of how that was handled (perhaps whether Japan would be warned first, and the timing of a second bomb, and the question of the Soviets, and potentially questions about the requirement for unconditional surrender) may have been quite different under FDR than they were under Truman. But we will never really know.