1. Plausibility check:
If Franz Joseph were to die heirless in, say, 1864 or 1865 would (or can) the Austrian throne fall to Maximilian, newly crowned Emperor of Mexico?
2. AHC:
If no, the challenge part is to make it so as plausibly as possible - even if you have to stretch...
3. WI:
What are the effects on intervention in Mexico with the Austrian navy and army now under the control of Mexico's Emperor? What about the nigh inevitable Great War? Long term effects on Mexico, Austria, America, Europe, and history in general?
Edit: Obviously the part of the agreement involving Max losing his Austrian nobility rights need be erased, forgotten, or negotiated out of existence. Is this task Herculean?