We look in on a town outside of Paris called Montfermeuil, which is totally real and still exists today. Now we find Fantine, who has given birth to a baby daughter and is living an incredibly harsh life.
No one will give her work if they know she's an unmarried mother, so she stops while passing through Montfermeuil and asks a random mother whether she would consider taking care of her (Fantine's) daughter. After some financial haggling, they come to an agreement.
Just like that, Fantine leaves her daughter with the Thénardiers. But don't expect a happy ending. They're are a pair of inn-keeping scoundrels who only look out for themselves and only agree to take Fantine's daughter because of the money.
Two years go by, and, as you might expect the Thénardiers mistreat Fantine's daughter, whose real name is Euphrasie but whose her mother calls Cosette.
Eventually, Fantine has trouble coming up with the money, so the Thénardiers put Cosette to work with totally age appropriate tasks like scrubbing the tavern floors at the age of five.
Cosette becomes known locally as "the Lark," because she is small and birdlike (probably from malnutrition) and always up in the morning before anyone else.