No power had a large enough army to be able to hold their gains when the American Civil War was over. Both Union and Confederacy had a much larger population and industrial base than either Mexico or Canada. Also, Mexico was busy going bankrupt, then being conquered by the French and then rebelling and Canada was part of the British crown, which had global commitments that made the notion of any rekindling of American conquests absurd. The cost of a large scale transatlantic war for European powers was far too high for any attempt to conquer or reconquer a chunk of American territory.

That being said, the French did try to take advantage of the lapse in American power to invade Mexico in the summer of 1861. By 1864 they had conquered Mexico and established a monarchy, but Mexicans never stopped fighting and begin to defeat the monarchy between 1865-66. The U.S. government provided surplus arms to the Republican (i.e. native Mexican) forces in Mexico after the American war ended in 1865, and clearly intended to not tolerate a European adventure so close to U.S. territory. In any case, the Mexicans kicked the French out completely in 1867 on their own without any major U.S. intervention.

This example is illustrative. The French intervention was fought with 6,000-10,000 French troops, a force which would have been dwarfed by the hundreds of thousands, perhaps even millions (records are poor) of troops fighting in the American Civil War. This stark disparity in military forces shows why no European adventure on US territory was attempted.

Because there was nothing for them to gain by doing so. Its important to remember that the US was at best a middle power until the end of World War Two. At the time of the Civil War, the only thing the US made that anyone else needed in any quantity was Cotton, traded to the British. However the British were able to see the writing on the wall that war was imminent years before it actually erupted, and invested heavily in Indian and Egyptian cotton to replace American output. Even if there had been an incentive for someone to want to try and grab something, it would never have been easy to do. Even if it had been easy, the expense of doing so would have been far too great. Wars were fought over vastly more productive and valuable places, like the sugar islands in the carribean.