Naval Problems and gatling guns
The USN was huge--but the ships were almost all coastal blockaders. I'd expect the French to control the seas completely outside of American coastal waters, at least at first.
While the US Army overwhelms Maximilians' troops, the navy will have to build a new generation of seagoing ironclads. Unfortuneately for the French, the North had the industrial potential to eventually flood the seas with them. If the war is still going on in 2 years, I'd expect the French to start having problems at sea as well. Now the European nations can fish in troubled waters at France's expence.
Also, the last French posessions in the New World end up under new management.
The Americsan advance into Mexico shows the world the potential of the Gatling Gun--IIRC, some rather reliable ones were available by this time.
Inside the USA, this could impact reconstruction. Perhaps the occupation of the South is moderated by the need for resources to clobber the French with? Parole a few generals, full pardons for anyone who fights for the US?
When the dust settles, the effects of the Sopanish-American war are seen decades earlier--the US has defeated a major European power, and can no longer simply be ignored.
Could Prussia decide to enter the war to defeat France once and for all? It might be worth while in order to get an in with the USA.