What practices did the French church at this time use to reform family behavior? How is that satirized in this play?
During this time period (1660s), the Catholic church throughout Europe was still having problems. Many works were written criticizing various aspects of the church. In Tartuffe, Moliere criticized religious hypocrisy, not necessarily the church itself. Tartuffe purports to be very holy when in fact, he is just the opposite. He is the worst sort of religious hypocrite. A very right-wing movement existed at that time within the Catholic church - Jansenism, which preached a very severe form of predestination (only the elect could go to heaven and this was determined before time began, all men were totally depraved, etc.) Moliere criticized this movement, which seemed counter to the concept of grace.
As far as family behavior, for one thing, the church frowned upon actors and playwrights. The church would not let anyone who acted on stage receive communion! Plus, many of the same things Martin Luther included in his 95 theses in 1517 were still going on - corrupt popes, Catholic clergy not obeying their vows of celibacy, selling indulgences, etc. So we see a satire more of the people that pervert religion, not necessarily the religion itself (some might disagree with this).
Also, examine how Orgon works with regard to arranging his daughter's marriage as head of the family, something sanctioned by the church. This should get you started.