I would think that the US would have been weakened by the conflict between its own people fought on its own soil. Is there evidence that any foreign government considered taking advantage of the situation?
Immediately after the civil war would probably be the worst time to attack. The US would have had about 2,000,000 unhurt, battle-hardened men who were, arguably, the world's only soldiers experienced in a "modern" war.
The Canadian colonies (who were in the process of negotiating their own unification), far from considering invading the US, were fearful themselves of a US invasion. The British thought an invasion was probable
In January [1865, British Prime Minister] Palmerston warned the Queen of 'the probability that, whenever the Civil war in America shall be ended, the Northern States will make demands upon England which cannot be complied with', leading to an invasion of British North America. In February, [Governor of New Brunswick Arthur] Gordon feared that 'the conquest of the South (which appears imminent) will be followed by a war with England'.
Far from taking advantage of US weakness, in 1865 many were wary of US strength
Britain and the Origins of Canadian Confederation, 1837-68, by Ged Martin
To add to /u/jianadaren1's comment, one thing to consider is the US Civil War was not a high casualty war like we tend to think of in Historic wars. In 1860, the population of the United States was 31,443,123 [1]. The total casualties of the United States Civil War ~646,000 [2], or 2%. Further, that is total deaths overall, combat deaths were quite a bit lower, about 214K, or less than 1%. There were plenty of able bodied men still able to fight after the war.
[1] https://archive.org/details/populationofusin00kennrich [2] http://www.va.gov/opa/publications/factsheets/fs_americas_wars.pdf