Franz Josef I was admired by many within the Austro-Hungarian Empire and was seen as the man who held the Empire together. His death lead to Charles I becoming the emperor, a devout Catholic who pushed the cause of peace. However, he did not have the same admiration as Franz Josef. How would Franz Josef living just a few years longer have affected World War I and the status of the Hapburgs and Austro-Hungarian Empire?
The continuing existence of Franz Joseph carries with it an immense cult of personality, one that is uncommon or nearly impossible to find in the post-WW1, pre-WW2 era. Kaiser was the only one capable of keeping the monarchy and the unstable union together at all costs. Though I can't see how he could have any effect on the World War itself, he could certainly keep the nations together even if on the losing side of it, as long as the Paris agreement wouldn't favor the nationalists of his respective nations (which would of course have hard time getting their agenda across with the old structures still in place, like they always had), but I also doubt Entente would encourage breaking up the union when that could potentially mean a strong German nationalist sentiment rising. Worst case scenario, A-H would be forced to cede certain regions to victors (Adriatic coast to Italy as per secret London pact of 1915), Bosnia to Serbia, large parts of Banat to Romania) but would not be messed with otherwise.