Plausability check, Prussians save US from Anglo French interventin in ACW

There was a query about the US joining the Central Powers. Is there any set of circumstances which could have Britain and France intervening the side of slavery and treason but, a little earlier than in OTL, Prussia going to war against France and distracting both Britain and France for long enough for the North to win?

Could this result in different alliances 1914
 
Prussia doesn't form the North German Confederation until after the war with Austria in 1866 so you would be talking about a Prussia acting without any of the southern German states and at least a third of the northern Germany...and no navy at all.

France would have little trouble and Great Britain might not even notice. Not to mention Austrian and Danish attitudes might combine with London and Paris to make Prussia very sorry it ever intervened.
 
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