In "Les Miserables," why does Fantine leave her child with the Thenardiers and believe that is the best decision for her daughter?

At the time of Fantine's decision, remember, she is a
single mother without a husband in a time when this was socially inappropriate.  She was
also poor and without means of a direct income.  In her mind, though her child was her
priority, she did not believe she could provide for Cosette at the
same time as taking care of her.  Who would hire a single woman bound by the
responsibility of a very young child?

She first saw Mm.
Thenardier with her two daughters playing nearby whom Fantine described as "pretty." 
They were in a rare moment of utter happiness at the make-shift swing their mother had
discovered for them, and from a distance, it was if Fantine was beholding angels. 
Pretty likely meant that they looked well taken care of.  In her desperation, Fantine
did not have time to do any sort of background check on this woman and her husband.  All
she knew was that they were married, had two daughters (about Cosette's age), and they
ran a small inn.

They of course seem very kind-hearted and
deceive Fantine into further believing in the goodness she had already bestowed on them
without reason.  Heartbroken and hopeless, she is in a hurry to start a life which will
be able to sustain the financial support of herself and her child, and in ignorance and
lack of experience, the Thenardiers seem like a God send.  She certainly believes she
will find stability rather quickly and assumes she will be coming back for Cosette very
soon.