Incentives? None...
NIII was deluded about Mexico; sending good money after bad after the defeat at 1st Puebla in 1862 is aan obvious illustration of that ... althoigh given that less than 4,000 Mexicans, mostly irregulars and volunteers, defeated 6,500 picked French regulars, one has to wonder about those who insist European intervention in the Western Hemisphere was a magic bullet for the Confederacy's strategic problems.
Even after the year-long effort to build up the French expeditionary force to 31,000 (which, again, suggests something about the ability of a European power to build up an expeditionary force in the Western Hemisphere, IMPERIAL STORM it was not) meant the French took until May 17, 1863, to force the Mexican forces at Puebla to surrender.
They then marched on Mexico City and took the city, although it was another year before Max et al showed up; at the peak of French strength, the entire expeditionary force amounted to 36,000 French, 9,000 mercenaries (Austrians and Belgians), 7,000 Mexican imperialists, and 20,000 guerillas - a grand total of 72,000, giving the French and their proxies all credit.
In 1865, of course, the US moved 50,000 troops to the Texas border, and the French made it clear they would abandon Max and the Mexican conservatives; NIII told Bazaine to negotiate with any Mexican Liberal he could find, other than Juarez, for a transfer of power, and had no takers.
The last French troops withdrew in March, 1867, and Max, Miramon, and Mejia were against the wall on June 19.
Even NIII could figure out it was a losing hand, against Mexico alone, by 1865-66; presumably that would have been made even more apparent, and even earlier, in a conflict with the United States ... as it was historically, since even NIII wasn't suicidal enough to try it.
Best,