How and why is the ending of TALE OF TWO CITES appropriately or inappropriately concludes the work?

The main thematic question of the novel is to what extent we can trust one another, to rely on one another's sense of morality. This is played out both on the small scale through the relationships around the Manette family, and in the large scale in the French Revolution. Especially in the latter, the most idealistic goals are undercut by the human ability to betray one another. So the ending is appropriate if you believe that humans are indeed capable of great acts of selflessness in the service of a cause - it is inappropriate if you think that Dickens does too strong a job of showing human viciousness, at which point you could argue it's sentimental. Regardless, its beautifully written and its survival as a classic scene suggests it works.