Ideally, after Britain and France agreed to join, other countries (Spain, Portugal, Netherlands, Mexico, hell all of Europe) would form some sort of alliance/agreement. While I dont see this happening(this IIRC didnt really start happening until closer to WWI) it would definetly help the south. Even if only 3 small countries could send aid it would be helpful.
But lets say only Britain and France join, and to add to the mess, the Netherlands and Spain declare war on Britain/France. This would severely limit the amount of troops that could be sent to America. But, it may be possible to simply continue the war in the america without any clear victor (trench warfare was used a bit in the war so lets say it became widely used). Then France can concentrate on Spain and Britain on the Netherlands. Lets be realistic, does the Netherlands really have a hope against the British.
So after a year and a half of war with Spain/Netherlands, troops can finally be sent to america in real numbers. Problem is now, some of the souths moral is down and the Union is entrenched. But the British navy has come out even stronger than it was a couple years ago. The additional 15 ironclads ordered 2 years ago have been completed(lets say the country is in overdrive) and a couple even saw useage late in the war against the Netherlands.
With these new ships, they are nearly able to eliminate the Union navy and most important ports have strong blockades. Given the nature of this non-attritional trench warfare, nothing is moving quickly. So the blockades have time to sink in and the Union army is stating to see its supplies dwindle. While the railroads have helped, things just arent moving.
France had some significant losses against Spain but a number of able generals made themselves be known and are willing to command a couple whole armies in the south.
The British public, after the defeat of the Netherlands, have really gotten into this war and the lines at the conscription centers are huge. This means an even more grand plan of attack from the north is hatch that involves the taking of norhern New England and the sacking of Boston. Let alone the normal bombardment of harbors all up and down the east coast.
After a year of blockade, the loss of much of New England and the burning of Boston, the moral of the Union has nearly collapsed. Except for Lincoln and much of the army of the potomac.
Late in 1867, one of Lincolns advisors comes up with a plan of attack against the entrenched EuroSoutherns. The plan is remarkable similar to what will occur in 50 years, attritional warfare.
Very soon both the European and Union ranks are severley depleted. Both sides agree to start ceasefire talks. While much of the North part of the Union is in British hands, so few defenders are left in the south that if the Union could manage to mount an attack, they might be able to break through. Fear of loosing the very point of this war makes the British and French agree to the Unions terms. The union gets its northern part back and the border of the CSA will be Missouri, Kentucky, and Virginia, not Ohio, West Virginia, and Maryland as the EuroSoutherns had taken.
It is agreed, and hostilities end. the CSA had 750000-1.2mil combat losses, the USA - 700000-1.4mil combat losses, Britian - 195000-300000 combat losses, France - 290000-320000 combat losses, Spain - 200000-250000 combat losses but over a million civilian losses, the Netherland - 25000-40000 combat losses.
I personally do beleive that if the war were to continue past 1865, trench warfare would become widespread.