Could you please tell me what is the meaning of Sartre's saying: "freedom alone can account for a person in his totality"? (Genet, 584)
He also means that you cannot dismiss the notion of free will, or you lose an element necessary to explain human behavior.
"Man is condemned to be free; because once thrown into the world, he is responsible for everything he does."
Whether or not free will is logical or compatible with our religious notions or even our physics, it is a necessary component of our psychology.
Responsiblity is an essential part of life, subjectively, and the domain in which human individuality is played out. It can be escaped only by dishonesty. So dismissing free will via philosophy, sociology, religion or physics is still a form of dishonesty.
Sartre is of opinion, "Existence before essence". This forms the basis of his assertion that humans are necessarily fully responsible for their action -- hence free. He said, "We are left alone, without excuse".
With these statements, he meant that there is no creator. Therefore, a person is free, and this freedom alone -- means there is no need for any other attribute, can account for him in totality.
Note: He didn't consider physical laws in not letting us free, I suppose. [pun intended]
Man's essence is freedom with or without a creator. Can you post the passage from Sartre's writings that you are referring to?
Physical laws may limit freedom but humans through knowledge understand nature and limit the necessity it impose on us.
Human's essence is freedom with a creator, because he is made in the creator's image, thus having spirit, which is a synonym with freedom. Man is free without a creator, because he is alone to choose his own actions and image, and he must do it in a good will counting on what is nature's best gift on him, his mind and his ability to guide his life without fear.
So i don't think Sartre derived the quote you are referring from an existential view point, but proposed the quote so to show how existentialism follows in harmony with what is regarded as a truth about humans nature and essence.
In the context now added by @Mathematician it is obvious that Sartre disliked the psychoanalytic analysis approach to human psyche (principle of pleasure, subconsciousness, repression etc) and Marx's limitations to the individual as a separate entity outside the community and tried to create a "no we are totally free" anecdote which in this context misses any deep philosophical ground.