If we look simply at the play named in your subject, Racine's Phèdre, we can provide an answer to this question based on a comparison of Racine's treatment and his primary source material, Euripedes's Hippolytus.
As Racine's title shows (though the drama was first titled Phèdre et Hippolyte), Phaedra herself has become the central character of the play. This in itself indicates an elevation of the status of women in drama and in society. Racine's portrayal of Phaedra is also quite different from Euripides's. In the Greek tragedy, she seems motivated chiefly by blind revenge. Racine's Phaedra is much more complex, and her agony is played out in such detail that in spite of her lies about Hippolytus and the tragic events they cause, she emerges as a wholly sympathetic character. One could argue that Racine implicitly shows that women experience emotion more deeply than men.
Two other factors are significant with regard to the increasingly enlightened view of women in the late seventeenth century. First, Racine adds the character of Aricie (Aricia) as the true love of Hippolytus. So there are actually two central, sympathetic female roles in Phèdre. Second, in Racine's version—unlike in Euripides's—Phaedra's death does not occur until the end of the play, when she succumbs to the poison she has taken. As such, the entire drama has revolved around a woman.
The very last couplet, spoken by Theseus, places Aricia as well as Phaedra at the center of the play's action and thus illustrates the theme of forgiveness stressed by Racine. Aricia is a daughter of the family of Pallas, the enemies of Theseus. Theseus's final acceptance of Aricia, his son Hippolytus's lover, indicates that some degree of healing is going to occur despite the immense tragedy that has unfolded:
Despite the plotting of her unfair family,
His lover, from today, will be my daughter.