If we have to have an actual failed D-Day on June 6 AND Germany still fighting a year later, we'd want to be more specific about the scale of the disaster - and why the Allies don't try again a bit later or push harder in Operation Dragoon, for example, to go through Southern France!
But again, let me throw in my two-cents ...
If D-Day fails, for whatever reason, but severely enough to throw planning back at least 2-3 months ...
a) The Allies are either ready to try again in the autumn
or
b) Push harder through Italy and Southern France first, followed up by channel raids and another DD-try in the spring of 1945
In both cases, you'd still have the Soviet armies deep into Germany proper in April-June 1945 - even if the WAllies haven't quite made it to the Rhine by that time.
About
25 per cent of the Wehrmacht were fighting the Western Allies from 1944-45 and the rest were fighting the Soviets. So even if the Allies fail to somehow establish a beachhead in S-France as well, you would still have to have divisions there to
i) fight them off and
ii) stay there to prevent them from coming back
Furthermore, you'd have to subtract all those men killed in stopping D-Day the first time around (that number might be considerable).
Thus, I doubt more than 10 per cent of the Wehrmacht could be transferred in this period to deal with the Soviets on top of the troops
already at the Eastern Front. That won't make much of a difference compared to OTL.
So by the summer of 1945 in this scenario - (with some very unlucky/very incompetent WAllies) - you likely have the Soviets at the Elbe, or slugging it out with Hitler Jugend and SS diehards in Berlin.
You also, all other things being equal, have a much harder nut to crack in Japan now - since nothing has changed ITL vs. OTL on that front in
this scenario.
In conclusion: The Bombs come online in July-August, and they would most likely still be used in Japan first, since Germany at this point is all but defeated. At most you will have the WAllies throw one or two 'demo-Bombs' - (cf. Calbear's point) - taking out a good chunk of the Ruhr or nearby - to make an impression on the Soviets more than anything else. (As if Hiroshima+Nagasaki won't be enough!)
That won't leave the post-war world much different, as I see it, from the first 3 options I suggested ... The Soviets have more of Germany, all of the Balkans and Scandinavia-minus-Sweden. France and Italy are severely hurt and seething with social unrest - esp. the latter. The US+UK will have to make a great effort to stop the Iron Curtain at the Elbe or Rhine and rebuild.
An interesting knock-off effect might be that a rump Western Germany will arise a few years after, and perhaps unite with the Benelux in a de facto federation, at least economically - foreshadowing the early EEC-constellation.
You might also see Italy breaking up, depending on whether or if there is a continuing civil war there, a la Greece, between fascists, communist insurgents and whatnot. Then again, the WAllies might decide to stay there and pour in a lot of military 'to protect the population' and insert a military government or some such.
But again ... those are just stray thoughts: The specific cause-effects and end-results would - obviously - have to be described if a full-time line at least since June 6 1944