IOTL, May 1905 saw Franz Joseph visiting a number of cities, including Mostar. It was believed that an assassination attempt was going to take place, but the Emperor went anyway and nothing happened. Let's say a situation similar to OTL Sarajevo happens and he is assassinated; the diplomatic aftermath goes to all hell and war breaks out; what are the sides and who are the players?
I am not sure we will get a general war in this case. The big difference is that it was not the unloved hair that got offed, but the head of an old respected royal family!
Also very important is who will do the assassinating here. And how will the alliances and givances play out.
Because I am unsure if the British are as deep in the French pocket and have as bad relations with Germany as later on. Also how secure are France and Russia towards Britain and each other? Not to forget, Italy may be more CP here... And that the Balcans are still more in the Ottoman sphere then later on.
Also how will A-H react? They lost their monarch and have all the reason to demand recompense and Imo most royal houses would agree, at least as a gut reaction directly after the fact. Later on it could change, but would A-H wait as long as OTL?
So in the end, the devil is in the details here as always in alternate history, without more information one could construct it both ways.
But for me, I think because it is so much worse then OTL, that the mayor monarchic nations will hold still for a time and that gives A-H the chance to act. And that it will act faster then OTL because FJ was afaik very well regarded internaly and externaly.