What major naval crisis nearly caused England to enter the war on the Confederate side?

Answer 1

There were actually two major crises.

The first was the Yankee seizure of two Confederate envoys to England -- off a British ship at sea. If Lincoln hadn't released them and apologized for violating English sovereign territory (her ship), it's likely England would have considered it an act of war and allied itself with the Confederates.

During the same period, several English shipmakers were furnishing ships to the Confederates, violating (in the view of Lincoln) England's claim of neutrality. After considerable protestations by the North, England ceased this activity.

Answer 2

There was a Navel blockade to stop the confederates from exporting to anyone. England was about to enter the war because they needed the cotton from the confederates. Had Lincoln not changed the reason of the war from preserving the Union, to abolishing slavery, England would have entered. They did not because they had just abolished slavery in their own country, so that would have made them a Hypocrisy.