Fantine gives Cosette to the Thenardiers because she is not financially stable enough to take care of both of them.
"Will you keep my child for me?' 'I must think over it,' said Thenarder. 'I will give six francs a month." (Hugo 45).
"Her clothes being gone, they dressed her in the castoff garments of the little Thenardiers, that is in rags. They fed her on the orts and ends, a little better than the dog, and a little worse than the cat" (Hugo 47).
Cosette is being treated poorly, like an animal. She is also dressed as someone very poor.
"This skirt made the Thenardiers furious...They gave the skirt to Eponine. The poor lark shivered" (Hugo 63).
The Thenardiers get upset because they did not receive money. The skirt was given to their own daughter, not Cosette.
"Cosette was ugly. Happy, she might, perhaps, have been pretty. Cosette was thin and pale; she was nearly eight years
Like Cinderella, Cosette is miserable living her life with her "family". Her misery worsens every minute with them.
"My child, that is very heavy for you which you are carrying there" (Hugo 157).
Jean Valjean comes in and helps poor Cosette, like her fairy godmother. Jean Valjean is Cosette's saviour from the Thenardiers.
"Suppose you were relieved of her?' 'Who? Cosette? 'Yes" (Hugo 174).
Jean Valjean is Cosette's godmother in this instance because he is freeing her of her misery.