My Opinion--If Hitler has nukes, he uses them against the Poles. If Poland has nukes of its own, it throws everything it has against Germany but probably doesn't achieve much. Germany has lost a couple of cities; Poland is in bad shape.
Now will Hitler go for Denmark--probably; that's not likely to result in a nuclear war. However, attacking westward against France means that you are going to have a massive nuclear exchange--and people like ITTL Manstein would know this and prevail upon Hitler to maintain the phony war--France doesn't nuke Germany, Germany doesn't nuke back.
Instead, with these tensions in mind, Germany launches an all-out attack against the Soviet Union, wiping out much of its nuclear arsenal and killing many of their largest cities. The Resultant war kills most of the inhabitants of Ukraine, Belorussia, Muscovy and the Baltic States--and the Wehrmacht bogs down only because the Soviets use nukes of their own to stall the other side.
By 1960, the war is mostly over as Germany is no longer able to fight. But 70% of the German People have died as a result of repeated nuclear bombardment. The Soviets have a lower figure, but up to the Volga they have suffered at least 40% losses. One Hundred Million People have died and far from the living space Hitler had meant to achieve there are now dead zones throughout Eastern Europe.
The War ends as Hitler is removed by the Wehrmacht, while Stalin and his politburo have been killed in the surprise attack on Moscow--the provisional leadership, led by Andrei Zhadnov calls for a cease fire with the German Military Junta in charge of Germany. Germany gets a chunk of territory from the Soviets, but its useless land poisoned by radiation for 150 years. Indeed, effect of this war creates a dead zone that is essentially impassable to humanity--for all intents a protective moat that prohibits a repeat war between the Soviets and Germany.
This world is going to suck..