That said, devastated by Indians? Didn't thin the Apache were that imperialistic at this time.
To be fair he could be talking about the Comanche who were raiding Northern Mexico with impunity for much of the era. Though I've always interpreted that as Napoleon saying the Native peoples of Mexico were incapable of self rule.
LN probably thought that it would take the US the best part of 100 years to pacify the Indians thus keeping them preoccupied. Plus they were embarking on their Civil War which would tie them up for the time needed to fully control Mexico.
He seemed to forget that
a) the Mexicans themselves might just object to being occupied
b) if the US puts its collective will into achieving something it generally does achieve it. Thus a shorter Civil War than might have been expected and the effective pacification of the Indians within 20 to 30 years.
Even if the French had managed to gain and maintain control of Mexico there would probably have been a US-France war over Mexico sometime in the late 19th Century. Which the US would probably have won unless the French had firstly come out of the alt Franco-Prussian War unscathed (I cannot see Bismark letting an opportunity like France being bogged down in Mexico going to waste!) AND they were backed by others (particularly Britain).
Well the entire ill conceived scheme was proposed to the Emperor and Empress by the Mexican conservative plant in France, Don Jose Hidalgo, who appealed to the Empress's sense of piety, who in turn appealed to Napoleon's delusions of grandeur. This convinced all the parties involved that the people of Mexico would welcome foreign intervention.
But you are quite right, even had France succeeded in their mission it would have led to long term strains with France and an eventual war between the two countries over power in the New World.
Just out of interest, would, if Max and Carlota had had a son, born on Mexican soil, have been a good or bad thing to the Mexican Empire/French Empire? Since the Mexicans might have the view that, the son is at least not European, or imposed on them by the French - although getting the Liberals to accept a monarchy in any form would be difficult.
A natural born heir would gave been a good thing for the nascent Empire since it would have given them some legitimacy. Unfortunately either Max or Carlota was probably sterile and thus they were incapable of producing an heir. They actually took the proactive step of adopting Agustín de Iturbide and his brother Salvador de Iturbide grandsons of the former Emperor Augustin I, whom he intended to groom as heirs.
The long term effects of this are hard to theorize on since the boys were so young and Carlota sent the heir apparent Salvador to France early on. I don't recall either ever returning to Mexico though.
Also, wasn't Juarez offered the Prime Ministership by Max at some point? Would L-N sign off on that, or did Max have independent power from France?
He was, which Maximilian would have had the power to grant, but he had no interest in serving a monarchy.
Maximilian and power in Mexico was a delicate thing. Technically the French forces in Mexico were subject to Maximilian's authority, but their commander Bazaine exercised almost as much authority as Max himself and would constantly ignore or go around Max's objectives. His main goal was to further French interests, and only help Max as far as those interests were served. OTL by 1865 he basically started to undermine Max's rule in line with the French policy of withdrawal.
European power, in particular French and British, could certainly still have been decisive in North America in the 19th Century... but only if there was a substantial local ally that they were backing. Old mate Max was certainly not that. And neither were there many examples at all of that throughout that particular century though that is a different question in itself to technical feasibility of trans-Antlantic power projection using 19th century tech. Still, in theory an incredibly powerful navy combined with often reasonably skilled/well equipped armies i.e. what the European Great Powers fielded relative their American cousins could well have tipped a balance in a contest of equals in the Americas...
It's rather important to note that by 1865 the French had overrun 2/3 of Mexico and Juarez and his forces were on the ropes for lack of arms and funding. It wasn't until solid American intervention in late 1865/early 1866 that things started to change as the French withdrew.
Absent that it was only a matter of time before Juarez found himself out of money and arms (and would probably have seen a number of his supporters desert to the Imperial cause like what happened in 1864) and his efforts to stave off French occupation would collapse.
That being said, while France would certainly have been capable of overrunning and occupying Mexico, the question of whether Max could establish a stable government and regime is another question entirely...