In Moliere's The Misanthrope, the rationale behind the character of Alceste is to show how difficult it is to go "against the grain". In this case, a man with extremely high moral values as Alceste intends for his social peers, a group of superfluous and careless aristocrats, to change their ways and live a life of honor.
The best way to treat this theme is to make Célimène as Alceste's love interest and, at the same time, as his foil. She is the complete opposite of him; she gossips, judges, criticizes, and insults just about anybody she wants. Yet, there is more to this...
In other to accentuate the true attributes of Alceste's character, Moliere has to put him to the test: to fight his angst against his love for Célimène; to compare his own judgement of mankind to Célimène's own penchant for judgement. In the end, Alceste wins the task by losing: he has to admit that he has the same potential for weakness as his love interest and, by default, he gladly forgives her. What this means, in not so many words, is that it DOES make sense that Alceste would forgive his girl: he has actually learned a lesson from her about his own weaknesses.
Moliere, who basically constitutionalized the style of French playwrights and authors, has an artistic tendency to build three-dimensional characters. It is a consistent occurrence in French literature. French Lit characters are hardly ever one-sided, nor flat; they are dynamic, deep, and understandable. This is the reason why they are allowed (and meant to) change and show their humanistic traits. As a result, the audience forgives them and even empathizes with them.