Felicite herself might be a symbol for purity and goodness. Literally, there is no evil in her, no machinations, and nothing that resembles an ulterior motive.  This is seen in her selfless devotion to Madame Aubain's children, as well as her willingness to provide care and comfort to anyone and everyone without hesitation (Including the parrot.)   Her name is representative of the spirit she possesses, and the opposite of what her world offers back to her.  She is the anti- Emma Bovary, Flaubert's most notable heroine.  I think that the parrot carries with it symbolic representation, as well.  Felicite sees it as a dove, a symbol of her religious faith.  Yet, I think that the bird, itself, can be seen as a symbol of the fleeting love that exists in the world in which Felicite lives.  The bird's brief escape from Felicite and his eventual death both represent the fact that love in the world that Flaubert describes is rare, transitory, and flighty.  It is only represented with Felicite, while so many display the opposite of it.  Paul is a good symbol of this.  Though doted with love by Felicite, he shows little reciprocation as he falls into drunken debt and then when is collected, moves to repossess his mother's belongings, showing little care for Felicite.