Coming to a different conclusion is certainly possible, implementing it may be a little more difficult even in an alternate history setting. The war of 1859 is a very good example: the Prussians decided to come to the support of Austria under the clauses of German Confederation; unfortunately their mobilisation was so slow and badly planned that they started having serious numbers of troops on the Rhine only after the war was already over. Pity.Stating that France would not do A or B because they did not do them kind of goes against the point of alternate history discussion. Its perfectly possible for Napoleon III to come to a different conclusion, more in line with his instincts.
In meaningful terms, this might mean that Prussia has to send some considerable force to the Rhineland, and loses Sadowa. If its a narrow victory for Austria, then the war begins to drag, but if we are talking worst case scenario then its the Crown Prince being defeated and killed on the field of battle, and Austria able to advance.
Coming to a different conclusion is certainly possible, implementing it may be a little more difficult even in an alternate history setting. The war of 1859 is a very good example: the Prussians decided to come to the support of Austria under the clauses of German Confederation; unfortunately their mobilisation was so slow and badly planned that they started having serious numbers of troops on the Rhine only after the war was already over. Pity.
It gets better than that. At one point during the Battle of Konniggratz Wilhelm, Moltke, and Bismarck were gathered together on a hilltop discussing matters when they suddenly found out that it was within range of the Austrian artillery thanks to several shells landing close by, forcing them to make to make a rapid and less than dignified departure. Simply have an Austrian gunner be slightly luckier and suddenly the Crown Prince, commanding Field Marshal, and Chancellor are dead in an explosion of blood, gore, and bone. Considering how close the battle was something like this could upset matters, at which point the Prussians would be retreating under less than ideal discipline, having to pass through an awkward narrow mountain pass, and then territory that they had already picked bare of supplies on their way to the battle.Worst is that Bismarck is killed by the bullets that missed him OTL...
Bismarck had secured the Russian benevolent neutrality well before the beginning of hostilities, same as it happened in the Franco-Prussian war of 1870. OTOH, relation with Austria were much less friendly, not just because of Crimea and the potential conflict of interest in the Balkans but also because during the Polish insurrection of 1863 Austria had joined France and Britain in berating Russian repression.
No chance at all of Russia intervening against Prussia in either case.
In 1866 Nappy was not ready to intervene, preferring to play the role of the peace broker and wrongly believing that France might receive post-war compensations from Prussia (which Bismarck had hinted about during the Biarritz meetings of 1865, without however committing to anything firm). Anyway the glacial pace of French mobilisation would not have allowed him to deploy troops on the Rhine before the end of the war.
Russians were shortsighted.
Allow the birth of a new great power (and potential menace)next to them,when they could crush in the cradle.
Same for France.
If Prussia had been destroyed from a great alliance of Austria,Russia,France in 1866,the war of 1870 (and the fall of French II Empire),and WW-I (with the fall of Czarist Empire) would have been avoided.
Austria would check the German States,and a balance of power could be achieved between the three Empires.
Russians were shortsighted.
Allow the birth of a new great power (and potential menace)next to them,when they could crush in the cradle.
Same for France.
If Prussia had been destroyed from a great alliance of Austria,Russia,France in 1866,the war of 1870 (and the fall of French II Empire),and WW-I (with the fall of Czarist Empire) would have been avoided.
Austria would check the German States,and a balance of power could be achieved between the three Empires.