Not heeding Britain's advice, Napoleon III aids the Confederacy and pays for it dearly.
At the battle of Chancellorsville French soldiers under orders from Emperor Napoleon III of France begin to help Southern troops attempt to take victory from the North. Thanks to France's support Stonewall Jackson isn't killed and General Lee makes plans for his invasion of the North.
At Gettysburg the battle goes just as the OTL states it does but then five minutes to Pickett's Charge General Longstreet delivers orders to General Lee from Richmond stating that the French have the intent to conquer the South should it gain independence and General Lee was to negotiate a cease fire with General Meade and all French troops were to be taken prisoner.
President Lincoln and Jefferson Davis meet in Charleston, WV and draw up a peace treaty that will abolish slavery by 1876 and allow the South to rejoin the Union without facing horrible reparation payments. Following this newly appointed U.S. Army commander U.S. Grant and his new second in command Robert E. Lee force all French forces out of the South and draw up plans for the U.S. invasion of French allied Mexico.
General Grant's, Lee's, Stonewall's, Johnston's and Beauregard's Armies began a massive push into Mexico wiping out every French column they encounter while slowly conquering every Eastern port in Mexico, destroying the French armies hopes of evacuation. Meanwhile, J.E.B. Stuart's Cavalry with assistance from Mosby's Raiders seize Monterrey back from French troops who had taken it early in the war. Finally, after Joshua Chamberlain held the American lines at the battle of Mexico City, William T. Sherman was able to march to the Guatemalan border in a 60 mile wide path of destruction that would simply be called Sherman's March. Shortly afterward the last of the French army in North America, pinned down on the Yucatan Peninsula by General Grant's combined force and a small British Army in Belize, which decided to try to have all of Belize join the U.S. after seeing that the U.S. would be a far better ruler then Britain, along with the newly freed Confederate Navy, which was now the Southern U.S. Navy, forced the last French troops to surrender April 9, 1865.
Napoleon III and President Lincoln met in Havana on April 14, 1865 to discuss peace terms for the war. France would have to surrender all of its American and Pacific territories in return for the French troops taken prisoner during the war, troops Napoleon needed badly to hold onto France's other imperial claims. Napoleon agreed to the terms and by July of 1865 the U.S. had annexed all of France's American and Pacific territories.
The U.S. would go on to conquer all of Central and South America along with the Caribbean, using the newly captured French lands as starting points for the different invasions. On July 4, 1876 all Americans, black and white, celebrated our freedom as the 13th amendment, abolishing slavery, was put into effect. Relations with Britain and France soured for about 20 years but come WW I and later WW II old rivalries of the 19th century were replaced by a new triple alliance of the 20th and 21st centuries.