That's two major industrial powers plus Mother Russia on Germany's flank as a bulwark versus two under-developed messes and France where everything important is within easy striking range of Germany.We all know that Turtledove really wanted the aligned Entent-Confederacy and Central Powers-US respectively.
We - as readers - do have the benefit of hindsight though.
For better or worse, how we look at it would probbaly be something like this:
With Habsburg monarchy in Mexico, sponsored by the French, we most likely have a France/Austria-Hungary alliance, which would most likely set off warning bells in GB/UK. THis means that the UK/GB will send more men to Canada upon Confederation to properly secure it, and quite possibly they will try and repair their relationship with the US - probably play the neutral party to both the US and CS respectively - I mean the entire commerce trade through New England alone has to be thousand time more valuable than a lot of the Confederacy trade of Cotton. Nevermind the mid-western food basket states.
I think with a more neutrally-inclined GB, France is going to support the Confederacy in order to secure Mexico so there would be some concessions and most likely means we can keep Nappy III on his throne (whether or not this stops the Franco-Prussian war is debatable, but that will always be up to interpretation). So we would have a CS/France/Austria-Hungary alliance in the latter half of the 19th Century.
Now this makes both Germany/Prussia and also Russia wary. Russia was incredibly pro-Union during the Civil War and I don't see too much reason why that would change, but because of the CS/F/AH alliance, Prussia and Russia are most likely going to form some alliance themselves. Russia wants Galicia, and Prussia wants all of Germany. a French-AH alliance pretty much disrupts all of that. I would like to think that the whole German Unification will see some similarities with the Union, at least to some degree, most likley they will both have close relations to the Union.
This also goes back to where the UK goes though. Trade with North America is essential as is keeping Canada. But at the same time, it has to wary of the European Powers. France could be just as likely to build a strong navy in this ATL like Germany did in OTL - or that could still be the same with the German-UK naval arms race. Ukraine does provide a lot of food so it may be essential to keep on good terms with Russia at the same time. And then you also have to consider that GB/Prussia/Russia all have intertwined royal families. And that alone is subject to change because come 1900 Frederick III could still be alive and could have tried to liberalize his country a bit. Queen Victoria also have two assassination attemts after the POD, 1872 and 1882 respectively. ALso Franz Josepf and Wilhelm I also had attempts on their life.
Butterflies are boundless really, yet I digress a bit ...........so I would think that if we have an alt-WW1 it would be:
France
Confederacy
Austria-Hungary
vs
Prussia/Germany
Russia
United States
Great Britain/UK is the neutral and its weight of power would determine the outcome if it chose a side.
Even if the UK joins the Franco-Austrian-Confederate entente, I think the balance is slightly in the *Central Powers' favor.