Your thesis statement focuses on the two major symbols of Chopin's The Awakening: birds and the sea. What your thesis is missing is a more specific claim about how these symbols connect to the novel as a whole, or how they contribute to the novel's themes.
Both birds and the sea are, as you note, related to "Edna Pontellier's new life." However, you don't say yet how exactly these symbols allow Chopin to "emphasize" that post-awakening life.
The sea is a bit more obvious as a symbol. The sea is described as "sensuous" and it "speaks to her soul." Being at Grand Isle that pivotal summer, Edna becomes aware of her more instinctual self, the self that does not want to expend energy to conform to the society around her. Though she only comes to this awareness gradually, and maybe even only then in part, the narrator tells us that this is the effect of the sea on Edna. And it's no surprise that it's a natural element that awakens her senses.
Bird symbolism is more complex. The novel starts out with a bird in a cage speaking French. The bird comes to symbolize Edna, and birds continue to be associated with Edna. The other most significant scenes related to birds are when Edna visits Mademoiselle Reisz and she feels Edna's shoulder blades to see if they are strong enough for "flight," and the corresponding scene when a bird with a broken wing flies over Edna as she swims into the Gulf of Mexico to commit suicide. The reader is left to wonder whether Reisz would see Edna as a failure in that moment; perhaps she was not strong enough to escape the strictures of society.
A more specific thesis would deal with the complex meanings of the symbols and would be explicit about how the symbols relate to Edna's character development in the novel as a whole.