The French had their eyes on Mexico at the end
The French had their eyes on Mexico at the end of the 1850s, because of the "opportunity" the Reform War (a bloody civil war, actually, that ended in victory for the Mexican liberals) presented them with the Mexican conservatives as potential allies. The Convention of London was signed in October, 1861, which cleared the diplomatic decks in Europe for the French intervention, which began before the end of the year. By the spring, the intervention had become an invasion, which led to the defeat at Puebla of some 6000 French regulars by some 4000 Mexicans, mostly irregulars. It took 12 months (1863) for the French to deploy enough troops (~30,000) to try a second time, and the conflict became a long, drawn-out, bloody, and costly conflict that ended in utter defeat for the French four years later.
So, given the historical case study presented by the 2nd Empire, odds are that even if someone in Paris was daft enough to suggest it seriously, the realities would rapidly intrude.
The Atlantic is not a river crossing. Considering that the only time any power actually managed a successful trans-Atlantic campaign in the Industrial Era was in 1917-18 and 1942-45, and both of those efforts were by the U.S., and both occurred with industrialized powers as ALLIES in Europe, one wonders when reality will ever intrude...
Best,