In my estimation, you'd have to change the Battle of Gettysburg and thus prevent the Anglo-French intervention that followed it in the weeks after.
According to the Post-War memoirs of Confederate Captain Samuel R. Johnston, the officer who conducted the early morning reconnaissance for Longstreet on July 2nd, he very nearly did fail to report that the planned road for Longstreet's march crested a ridge where Federal observers on Little Round Top could see it. Had he not accurately reported such, Longstreet's forces would've been forced to counter-march once they discovered this, throwing the attack time tables off and pushing his attack later into the day. This would've likely exhausted them before they could even get into combat, given the expanded distance would've been close to 20 miles. Further adding to this, Union Major General Daniel Sickles was planning to move his forces forward due to the poor terrain of the defensive position he had been ordered into, but Longstreet's attack beat him to doing such. So, not only would Longstreet's men be tired, but Sickles would inadvertently spoil their planned attack by moving his men forwards, and the combination of these two things would probably be sufficient to save the Federals lines that day.
Such would be a massive change from what we know did happen IOTL that day, which saw Longstreet's movement go off relatively perfectly. His 13 Brigades, after a short period to rest and fetch water, jumped off and attacked downhill on the six brigades of Sickles, whom were stretched out in a line and had no integrated artillery support due to the boggy ground and the poor elevation of their position. Longstreet's attack effectively cut the Taneytown Road and managed to, in conjunction with Ewell's own offensive, surround and destroy the Union's 1st, 2nd, and 11th Corps. Stuart's arrival later in the day allowed Lee to thereafter destroy the bridges over the Rock Creek, and thus further destroy the 6th and 12th Corps after their route of retreat and resupply was thus removed. Only the 3rd and 5th Corps managed to escape the disaster, thanks to their position on the southern portions of the Taneytown Road, which allowed them to retreat to the Pipecreek Line. In the weeks after, as we all know, Harrisburg and the local coal mines were set ablaze and Philadelphia was occupied; such ultimately led to the passage of the Roebuck Motion in the British Parliament and the subsequent Anglo-French intervention that ended the war.
So, without Longstreet's success that day, we can presume Lee at best manages to pull off a tactical draw or slight victory and thus the Roebuck Motion
might stall out. Without the Anglo-French intervention, France would've not firmly tied itself to the Confederacy, obviously, which would've removed its principal ally in dissuading aggressive American actions against their (The French) forces in Mexico. IOTL, this alliance, which threatened the United States with renewed warfare with both the Confederacy and their French backers, led to steep decline in American support for Juarez. Without such a decline of support and perhaps with
butterflies saving Juarez from capture after the defeats of November of 1863, the Republican cause could've likely remained more unified and thus effective instead of degenerating into the disorganized partisan bands as it did IOTL, which caused the French enough trouble to keep them occupied, but not enough to force them out-in other words, a quagmire.
What effect this has on Europe, I cannot say, but at least I think I've given you a basis on how such could be setup.