There were a couple of TLs several years ago that looked at Union-British conflicts. Taking opposite views of the consequences for the Union! One thought the Union could brush aside any land forces Britain had and respond to a blockade by forced industrial expansion. The second had more or less the opposite viewpoint.
Sadly, the two authors were banned and the TLs were ended short of a finale.
FWIW, my view is that a lot depends on the timing and nature of the PODs causing the war. And what influence the French had on the goals of the Allies/Co-Belligerents.
Left to itself I think that Britain would seek a limited conflict, concentrating on blockading the Union's Atlantic ports and defending Canada. It had no real interest in helping the Confederacy gain independence, despite King Cotton. The Northern States were more important trade partners and destinations for investment while public distaste for Slavery was also a factor in political calculations.
The French might be more willing to directly aid the Confederates. Breaking the Union blockade and supplying munitions but not troops I think. Their main goal was Mexico.
So unless something causes both Britain and France to make all out war on the Union with CSA independence as a war aim..... then my guess is both Britain and France get minor concessions from the Union at the time. The Civil War lasts a bit longer before a Union victory. (Unless Lincoln loses the 1864 Election to a Copperhead.)
And the reunited USA becomes hostile to Britain and France which affects events for several generations.
I think if Britain fights this war to win they would win.
Canada had a similar sized population to what the confederacy had minus the slaves. Thus Canada could muster a similar sized army to the confederacy.
Britain could also send it’s own troops. During the second Boer war Britain sent 350,000 troops which were from mainland Britain to South Africa. The U.S civil war was less then 40 years earlier so I don’t see why Britain wouldn’t be able to send a large force to Canada.
The British would also have naval superiority so could brake the Union blockade and maybe even raid the coast.
If the french get involved they could perhaps send some troops to aid the confederacy. Imagine if the confederacy gained a french expeditionary force. This has the power to turn defeats into victories.
I think if Britain enters this war with the clear goal of helping the confederacy gain independence and hampering U.S influence they would win.
It was actually a massive geopolitical blunder for Britain and France (especially Britain in the long term) not to get involved imo. They could have severely weakened the U.S and stopped it’s rise as a great power. France would also have reason to be involved as the U.S was against their intervention in Mexico and in our timeline after the civil war had finished the U.S forced them to withdraw, dooming Maximilian.
