Why do you suppose Racine wrote the play in rhymed couplets?
Racine was part of the French neoclassical tradition of the 17th century, in which theatre artists returned to the Greek myths for inspiration. One feature of their source was order, by which is meant a sense of propriety, of balance, and one very effective way to indicate order and purpose is to find a natural rhyme to words, giving them a direction, and denying any chaos or accident. The rhymed lines in couplet form give the listener a sense that the dialogue follows a reasonable logic beyond mere human speech; all the neoclassic poets, through the 18 and 19th centuries, to Modernism found in rhyme this same orderliness. It was only with such poets as Eliot and Whitman that the tendency toward rhyme was broken. In addition, when spoken, a rhymed couplet sets a mood for the characters, a mood of gentle expression, of reasoned and controlled emotion. Phaedra’s story is suited to this expression.