WI William Henry Seward is elected in 1860 and somehow manages to avoid the Civil War (perhaps he follows a strategy of allowing slavery to die out on its own, as Lincoln was considering).
In OT, Lincoln had supported Juarez, but was unable to invtervene due to the Civil War. After the war, President Andrew Johnson did send 50,000 troops under the supervision of Grant and led by Philip Sheridan, where they ran patrols to threaten the French.
Without the Civil War, however, it's possible that the United States might have been directly involved in a war against the French in Mexico-perhaps with Grant and Lee commanding their two armies on the same side! Not to mention the skills of some of the other Southern Generals (who would probably be Colonels here) since some of them, including Lee, were veterans of the Mexican-American War.
The war lasts from 1862-1865 (or thereabouts). It has the effect of turning America into a world power thirty years before the Spanish-American War, and perhaps gives the United States an earlier excuse to annex Cuba and the Philippines. The Southern states, having been cut off from the West, try to find a new source for cotton plantations (and the de facto expansion of slavery) in South America, but the War of the Triple Alliance puts an end to such plans. By the 1870s, slavery is a dying institution and ends altogether in 1877 (although the struggles of African Americans parallel those in OT otherwise).
Thoughts and comments are welcome!