So there tends to be a lot of discussion about how likely European intervention was, with an implicit idea that it would have changed the outcome. Lets assume for a moment that Britain and France decide to intervene, what would it have looked like, and would it have changed the outcome?
I tend to think it would have created a mess, but I'm not sure it would have impacted the eventual outcome.
Reason 1: Union mobilization... In the words of Shelby foot "the North fought that war with one hand tied behind its back." A wider war with a risk of invasion would have, in my mind, led folks in the North to rally around the flag. The US probably could have raised armies to make a serious bid to invade Canada, while still carrying on the war in the South.
Reason 2: Distance: Any Anglo-French intervention would have to be supported across the Atlantic, which is no small task...especially in the presence of the Union's rapidly growing naval power. This would greatly limit the number of forces involved. If you look at the French intervention in Mexico, we are talking about an expeditionary force of 20-30,000. Are a couple of French or British corps going to turn the balance?
Reason 3: Other concerns: If the ACW was the only concern of GB and France, perhaps they would have made a major effort, but they both had other global concerns. For France, Prussia is on the move, and the more forces sent away weakens its position in Europe. In 1870, the country falls to Prussia, even without forces spread out in Mexico, Italy, Algeria and other points. GB has the empire, India, and the Great Game with Russia to worry about. Both Bismark and Russia were strongly pro-Union, so any intervention force would have been put together with the need for these powers to keep enough reserves to protect their European interests.
Of course it would depend on how things played out on the battlefield, but I'm not sure the intervention of European powers would have altered the final outcome.