In terms of consequences, a significant one will be that many of Juarez's reforms will be stalled. Following the war with France, Juarez won the power to rule by decree, and forced through a variety of reforms, such as in education.
Absent the war with France, the Conservative position will be relatively stronger, leading to potential opposition to Juarez. Hard to say exactly how that will play out, but there could be significant changes.
Mexico would of course gain from not having the loss of life and economic cost of the war.
Well, one could easily get this by just having Juarez continue to service Mexico's outstanding debts. In that case, the Liberals likely win the Reform Wars by the mid-60's, though in such a way that the Conservatives aren't as discredited and utterly broken as in our timeline. McClane-Ocampo might also end up sticking, allowing for a post ACW Tehuantepec railway (likely a bone the Conservatives would pick at in the later battle for hearts and minds, particularly as the area runs close to native populated areas), and we'd see the ideological fight in Mexico take on an isolationist/Mexicans First/traditional economy vs. Export Economy "Poriferiato" style system.