well in the storyline we all know, its just a cosmic energy that takes jean as a host, but actually it doesnt even do that, it makes a clone of jean's body and acts in her place while the real jean lay in some coma some ocean ( see the similarity to the movie? ).
BUT this is the retconned story, in the original story jean DID possess the phoenix, it was just her maximum potential ( see another similarity to the movie? )