Well if you have the right POD then a war could occur. A lesser known fact is that Maximilian offered the position of Prime Minister to Benito Juarez. Now some can argue this was a trick, or unlikely to occur but given Maximilian's actions during his reign I believe he was serious in the offer. So if Juarez decided to try and work with the government it may have ended the rebel faction, and string of killings that followed the regime change.
So if you have a somewhat unified Mexico, with a little trouble but the conservative, and liberal factions in some form of compromise Mexico may stay a French colony for a few years.
Now with this POD in mind one has to wonder what the US would do. On the one hand France will leave, yet on the other a Monarchy that forced itself into power is in North America. I can see any number of Presidents mad at a monarchy sneaking into the area. So America says get out, Maximilian says no, and Juarez even says no given the land reforms passing, and much getting down while giving lipservice to the landed elites, and at the same time seing the issue of a monarch a Mexican problem.
So the war occurs in 1867-1869 and ends as everyone expects, but I could see Emperor in exile, and maybe even looked at fondly in the decades to come. Jaurez as the great compromiser, who found that nice niche to get reforms done, but without angering the wealthy.