Okay can we stop using a fiction book as the central idea for our discussion? Such things really go into other threads.
Now the idea here I think has some merit. First as history has shown us despit the nationalist ideas of the various ethnic groups in AH it has an underlying cultural identity. Let us assume FF dies, and just as a starting off point us Old HT's time frame of 1914. It works as a group of Serbians did in fact plot out such an action, and even train men to do it.
So the following are possible ideas.
1. Austro-Serbian War of 1914
FF dies at the hands of an obvious Serbian group. AH sees this not as a method of sorrow but a chance for the much coveted lands to the south. While Russia has a stake in the region, public opinion for monarchy infested Europe would no doubt have some feelings in favor of AH. So AH either makes a general demand and Serbia gives in, or the more likely event is that Serbia says no giving the AH forces reason to invade. It is a quick, won through overwhelming numbers.
Time goes on AH must now deal with not only the ethnic groups seeking freedom in their own lands, but the Serbs who have a template for a nationalist state. If the Great War still occurs as OTL we may see AH fall then and not in 1959.
2. Central-Entente War
This is interesting, as Russian has interests in Serbia and thus reason to defend it. Germany has an alliance with AH, France with Russia, and Italy with Germany. So in this matter the question is who strikes first? My money is on the Russians. They acted foolishly when confronted in 1905, did so again in 1923, and would no doubt assume their size would give them victory in 1914.
So Russia calls its forces up sending shockwaves through Europe, with nations responding in kind. It takes three weeks so in August we have Russian forces marching upon AH. This creates the ideal war many in CP wanted. In a time before planes - no matter what HT says pilots do not fly scouting missions and think "hey let's pull out a pistol and shoot the other guy" nor will it be endless trenches- the fight will be one of marching. The German plan was to swep into Belgium and then march on France. Italy has to fight as Russia invaded so France will face a two front war, and no doubt be defeated in a few weeks. Now Germany can focus everything East, Russia is lonely and will no doubt try for a safe peace.
3. Grand War
Same as above but with the UK involved. HT for some reason has the Italians as rather poor soldiers, and cowardly fighters. Yet looking back they had a military and an Empire above AH, and many other European nations. So Italy is obligated to help its ally out. When the Germans invade beligum the UK declares war on Germany.
France is still doomed to fail but maybe they last out half a year instead of a few weeks. Wth British help they can hold the German or the Italian front, but not both. Another interesting thing is how it is possible for Italy to fight the UK head on in Egypt, and over in Somalia. That will no doubt end in a British victory but given Italian naval abilities in the Med they should make the UK bleed. War ends around 1916-17 depending on how stupid the Entene wants to be.
4. Grand War Light
Same as above but the Uk stays out of Europe. They fight the colonies, and German shipping but no British set foot in France.
5. No war
Cooler heads can prevail, or a princes council can be set up to settle the matter. AH will be given a sliver of land and a apology. Serbia must be made to look the bad guy, but outside of future anger towards each other I cannot see major events changing OTL.
6. Long war
Let us assume for an instant that trenches really are impossible to get over. That the Turtledove Trinity cannot be broken like those books make it sound without tanks, or bombers twenty years to early. Well things get interesting.
First France may well hold out given its Empire, but the mixture of Germany, Italy, AH, and a friendly Ottoman Empire will no doubt give the Central Powers similar abilities.
So it becomes the war of industrial, skilled armies against manpower rich Empires. I call this the long war for I see it easily reaching the three year mark. Now a CP victory leads to more land, and the Entente dealing with years of their Empire's raising up. Entente victory perhaps leads to slightly more radical, or democratic movements. On the whole I favor the CP's, they had greater abilities and more over greater drive for victory. France, Russian, and the UK at war will deal not just with german machine guns, but Indians seeking freedom, African states rising up, and Polish or Ukrainians trying to get a better deal.