Great North American War

  I couldn't see the probably level of bloodshed or the union economy/willingness to continue the war lasting anything like that long.  If they did manage to attack Canada they do have some chances to make progress before British reinforcements arrive, see the TL I referenced earlier, but if they just sit back in the north then their economy is likely to collapse long before 1870.

  Also one other factor I forgot to mention yesterday.  The position of the south is going to be markedly stronger.  Even if Britain [and other European powers] don't recognise the south, which I think Britain may not do for a while the British blockade removes the threat to the southern coastline - which frees up forces.  Probably even more importantly, while the union is cut off from trade with Europe the south now has access.  So it can sell cotton and other goods and buy manufactured goods that it lacked OTL.  Including of course a lot of weapons, uniforms etc that it was short of OTL.  If in a year the union army is still using modified muskets, even those refitted to be sort-of rifles and the south is well equipped with modern rifles and artillery things are going to be a lot costlier for any northern attack.  Now that the union is fighting Britain the south could risk going onto the defensive and forcing the north to come to them.  [Risk because the UK and union might make a separate peace at some point.]

  If it gets to the point that Britain, probably followed by other European powers recognise the CSA or even worse Britain and the CSA have some sort of formal alliance then the southern position is even stronger.

Guys

I think assuming that Prussia will attack France under those circumstances could be risky. OTL after defeating Denmark [in alliance with Austria] then defeating the bulk of the German states, including Austria Bismarck manouvered to get France to declare war on Prussia. This was necessary to make France seem enough of a threat that the southern German states, nervous about Prussian aims, were willing to side with it against the French and then join the German empire established. If France is still emboiled in Mexico I can't see Napoleon III taking the bait. A naked attack on France by Prussia might well win - although there could be butterflies - but it could mean that the resultant German empire doesn't include the south German states [Bavaria, Wurtemburg and Baden] which could well form some sort of alliance with Austria.

If the war between the US [and possibly Russia but I doubt it] is somehow still going on by 1870 then its unlikely that will get linked up with a Franco-Prussian war. Britain still heavily involved in a war in N America is unlikely to distract itself by getting involved on the continent and similarly whoever wins on the continent is unlikely to wish to immediately start a new war with Britain.

Alliances tended to be fairly fluid in this period. France varied between friendship with Britain, hostility towards it and then friendship again as the two powers faced a common threat from Germany. Prussia/Germany was an ally [albeit fragile] of Austria, an opponent then a friend again. It often had good relations with Russia but clashing interests in eastern Europe drove them apart and if a strong Prussian centred Germany arrises TTL that is likely to occur again. Presuming that the US is defeated, as is likely, its likely to be hostile to both Britain and the CSA but how long that lasts would be variable depending on the circumstances. [International relations, internal developments in the rump US and the terms of the peace treaty will all be very important here]. Its likely that when a WWI type conflict occurs in Europe the US will be a lot less friendly to Britain but its far from certain either what the sides would be or that the US would definitely be fighting. Similarly there are a hell of a lot of paths an independent CSA could take.

Steve

So ultimately a Russo-American Hegemony would run the North American continent?

I believe the Russian Civil War, assuming it wasn't butterflied, would result in the total commitment of the U.S. military to fight Red Army.

How would the 20th and 21st centuries likely be affected by a Russo-American alliance?

Western Europe would probably be our primary rival in an alternate cold war?

So probably United Kingdom, France, Italy, Spain, and Portugal along with their colonial holdings against Russo-German-American alliance?

  Even if that happened, and it would seem unlikely, you then have things set up for them to fight over the spoils.  With the US winning in the short term but with a probability of lasting emnity between the two powers.  [Russia is too weak at this point to play a major role outside eastern Europe at most and definitely couldn't defeat a militarised and expansionist US in N America.]