~That's a good question, since the major battles and the most consequential battles occurred in the Western Theater. For instance, at the very same time that the Army of the Potomac and the Army of Northern Virginia were each doing their best, through incompetence and gross insubordination at the highest levels of command, to hand victory at Gettysburg to each other, Vicksburg fell to USA forces. The Confederate loss at and of Vicksburg was far more consequential and had far greater effect on the eventual outcome of the war than did Gettysburg.
Gettysburg marked the final effort of the Army of Northern Virginia to invade the USA and the needless loss of irreplaceable men and equipment there pretty much doomed Lee's army. On the other hand, if Meade had followed the orders of Abe Lincoln and General-in-Chief Halleck (and later, their pleas) and pursued Lee's defeated army, the Army of Northern Virginia would have been trapped on the muddy banks of the flooded Potomac, exhausted, without ammunition and provisions and with no means of escape. The surrender of the Army of Northern Virginia, and with it, the end of the war in the East, was likely and could have well been achieved in July and August of 1863 if only the Army of the Potomac had had a general in charge who had the willingness and guts to actually fight the war with an eye towards winning.
In my humble view, Gettysburg is significant because of what could have been accomplished but was never attempted, rather than by what did occur. I think equally significant was the accidental killing of Gen Thomas J (Stonewall) Jackson a few weeks earlier. James Longstreet was a far more savvy and competent strategist and tactician than was Robert E Lee, but by himself could not convince Lee of the stupidity of engaging Federal forces at Gettysburg (of course, the insubordination and disobedience of orders by Harry Heth and AP Hill more or less took that decision away from Lee in any case). Certainly, had Longstreet been in overall command, the battle would have been fought far differently (and far more intelligently). Had Jackson been alive and present, and assuming he and Longstreet could set aside their personal jealousies, it is more than possible that together they could have convinced Lee of the folly of his multiple poor decisions.
Then too, had Jackson been present, neither Jubal Early nor Richard Ewell would have been in position to hand Cemetery Ridge to USA forces on a platter. Without holding cemetery ridge, Hancock and Howard never would have advised Meade to engage his entire army in the battle. It is probable that Meade, only in command for three days, would have withdrawn and forced Lee to pursue him and then engaged on better ground. At the very least, Meade would have resumed Hooker's cat and mouse game of shadowing Lee's army until either Lee had to turn back for want of supplies or until an inevitable battle was joined on more defensible ground of federal choosing.
Examined carefully, the Battle of Gettysburg was a farce, punctuated by one incredible mistake after another. The amount and extent of stupidity, incompetence, arrogance, disobedience and insubordination exhibited there on both sides was nothing less than incredible. And all because Lee wanted a victory in the north, simply to convince northern politicians to terminate prosecution of the war (something they were close to doing, especially before Antietam/Sharpsburg the previous fall.
There never was any real worry that Europe would ally with the CSA. Great Britain was THE superpower of the day. No other nation in Europe was foolhardy enough to recognize, or even worse, to ally with the CSA and risk war with Great Britain by allying with the CSA and running the risk that the British would go the other way. As the US would do to them in WWI and WWII, the British were content to sit back and watch the upstart Americans bleed each other dry. The USA was becoming an economic and industrial force to be reckoned with, and was diluting British supremacy. [I won't go off on my usually diatribe on the fact that in 1860-65, the USA was not a single nation but was a confederation of independent nations or why secession was not only legal and a constitutional right, but was the central premise of the Declaration of Independence and why the war was an invasion and war of aggression by the USA against the sovereign nations of the CSA and why it was NOT a civil war.] Although not a military force to be concerned about, the USA was becoming a formidable economic foe and the war could only diminish USA influence regardless of the outcome. The northern confederation of USA nations was a far more beneficial trading partner of the British than was the CSA confederacy of nations. Even had Great Britain recognized the CSA, no alliance between them was ever likely.
Actually, the most significant battle of the war was the Battle of New Orleans in the Spring of 1862. The consequences of the loss of its most important city and port were incalculable to the CSA and with the loss of New Orleans, the CSA lost the war. That is, the war was lost once Lincoln found real generals, willing to fight, and willing to fight to win, in Hiram US Grant and William T Sherman. If any European nation was going to join the war on the side of the CSA, they, and especially the French and Dutch, would have done so as a result of Benjamin Butler's antics as military governor of New Orleans.
CSA armies, even the Army of Northern Virginia, continued to enjoy successes over USA armies after Gettysburg and Vicksburg. See, for example, Fort Wagner, Chickamauga, Charleston Harbor, Spotsylvania Courthouse or Cold Harbor. Lee was forced to give up his idea of invading the north, having been crushed in both attempts, first at Antietam/Sharpsburg and then at Gettysburg. Moreover, Grant knew that with the numerical manpower and industrial advantages of the USA, the CSA could not long survive a true war of attrition and even when the CSA won a major battle, it was at such great cost that the end loomed ever nearer. He saw the grave error that Meade had made at Gettysburg by not pursing the advantage obtained by victory in a major battle and he wasn't about to repeat the error, nor was he about to let his subordinates like William Sherman repeat it (and to insure that Meade didn't do it again, he accompanied Meade and the Army of the Potomac throughout the Wilderness/Overland Campaign).