At its simplest, The French Lieutenant's Woman is a love story, focusing on the relationship between Charles Smithson and Sarah Woodruff.  But it is also a reflection on the whole Victorian era and the forces that ended it.  John Fowles broadens our understanding of Victorian society with digressions into the controversy surrounding Darwin; the change in relations between the classes and the sexes; the era’s complicated sexual mores; and myriad other elements of Victorian intellectual, political and social culture.  A variety of supporting characters (particularly Charles’ servant Sam) offer a more fully-rounded picture of the age.

At the novel’s start, Charles is visiting his fiancée in Lyme.  Ernestina is the spoilt and shallow daughter of middle-class parents who have made a great fortune and now wish to elevate their child to the upper classes.  Charles is an intelligent but idle upper-class gentleman who is in line to inherit a title upon his uncle’s death.  While in Lyme, Charles meets Sarah and is told her story: she was seduced and abandoned by a French sailor and has since been an outcast in the straitlaced provincial town.

Charles encounters Sarah several times during his stay in Lyme and finds himself drawn to her, struck by how different she is from other women.  She is intelligent and independent at a time when the ideal woman was submissive and fragile.  Charles’ aversion to the less typically Victorian aspects of Sarah’s character vies with his increasing fascination with this unconventional woman.

Events come to a head when Charles loses his chance of inheriting his uncle’s title and Sarah loses her job as the companion to a bigoted old lady.  In the dramatic aftermath of these developments Charles realises the depth of his feelings for Sarah.  He decides to break his engagement with Ernestina and marry Sarah instead, sending word of his intentions to Sarah via his manservant Sam.  For his own reasons, Sam does not deliver this letter.

When Charles looks for Sarah after breaking his engagement, he finds she has gone away without leaving any word of her destination or any explanation.  He searches for her in London, Exeter and Lyme to no avail.  After several months of demoralising failure, he abandons England and travels across Europe, the Middle East and the United States.  His travels allow Fowles to broaden the novel’s portrait of the age even futher.  Although travel lifts him out of his depression, Charles never forgets Sarah and he returns to London immediately when his lawyer sends word that he has found her.

When Charles finally meets Sarah again, the story splits, with the author offering two alternate endings for their relationship and leaving the reader to decide between the two.

For a more humorous – and scathing – summary, try this Guardian article.