Bismarck would never have allowed the continent to split into two competing alliances. The Kaiser had thought that being related to Tsar Nicolas would allow them to maintain peace between their countries based on their personal relationship. Bismarck would never have made that mistake. He would have certainly not allowed the German alliance with Russia to fail and so allow Germany to end up with enemies to either side.
This changes everything.
In the years leading up to 1914 the French had been pouring money into their Russia, resulting in a fast rate of industrialisation. The German high command estimated that if industrialisation continued at the same rate the Schlieffen Plan would soon become unworkable. This is one of the reasons that von Moltke had been so eager for war in 1914 while the plan still had a chance of working. But with the Alliance of Three emperors still in place, there would be no French money pouring into Russia, nor would there be a Schlieffen Plan for Russian industrialisation to upset.
It is likely that a conflict between Germany and France would eventually erupt due to the French having unfinished business from the Franco-Prussian War. It is also likely that the French would have an attack plan similar to Plan XVII because this plan is the quickest way to secure their objectives of recovering Alsace and Loraine. The German plan on the other hand would look nothing like the Schlieffen Plan. They would not need to knock out Paris quickly in order to turn their army around and deal with Russia, because Russia was not a threat. Therefore they do not make their strike through Belgium, which keeps Britain out of the war. The two strongest armies in Europe run straight into each other in south-eastern France. It starts as a war of movement, but it quickly bogs down into a network of trenches that stretches between the borders of Switzerland and Belgium, and the two great powers start to bleed each other to death just as Jan Gotlib Bloche had predicted.
This is a war that can only end with the complete destruction of at least one of the belligerents' societies. In real life this turned out to be the members of the Triple Alliance, but this time I would think that it would be France. Germany had been able to hold back both France and Russia at the same time, loosing mainly due to being starved into submission by the British blockade. This time they would only have to fight France, and Britain's role in the conflict is to sit on the side-lines sipping tea while they sell war material to both sides in exchange for hard currency.
The war ends with a mutiny in the French armed forces (similar to the Kiel Mutiny), but it quickly escalates to a full socialist revolution (similar to the Russian Revolutions). The French political structure shatters dozens of different groups, and as most of them are armed they soon start fighting amongst themselves for control (like the Russian Civil War). The colonial powers exploit this situation to grab former French colonies. After years of fighting Germany is too weak to really exploit the situation and only manages to get a few bits of West Africa and maybe French Indochina. Britain on the other hand is now by far greatest power in Europe. It quickly gobbles up the former French colonies on the southern Mediterranean and turns them into protectorates (as happened to the Ottoman Empire).