French intervention in Mexico: cost and an alternative force

Why did Napoleon III undertake a costly invasion of Mexico instead of holding Veracruz, and how did the costs compare?

The invasion is judged more expensive without a numerical comparison. A larger French deployment supporting a substantial Imperial Mexican Army is proposed as a possible route to victory.

The full intervention is judged more expensive than the questioner's proposed limited occupation of Veracruz, although no comparative cost figures are supplied. France's simultaneous operations in Vietnam complicate the casual description of Mexico as its Vietnam. The alternative scenario assigns 100,000 French troops to the border, important ports and mobile response forces. An Imperial Mexican Army of 200,000 to 300,000 soldiers would provide much of the remaining strength. Victory is considered probable with that force, without a detailed campaign calculation. Both sides' leadership is criticised for distrusting soldiers beyond direct oversight and therefore failing to coordinate guerrilla warfare effectively. That criticism concerns command arrangements and expressly preserves Mexican troops' ability to fight guerrilla campaigns.