Greek and Latin poetry does not require rhyme (although it does use it, it's seen in classical antiquity from Homer to Virgil) because the Ancients do not think the "verse" as the same unity as we do. But the inversions could be there to accomodate the rhyme, not the opposite.
Most romance languages lost a good part of their syntactic freedom as they passed from 16th to 17th centuy. 16th, with religion wars, was overflowing, chaotic. It's heavily reflected in poetry. Compare Montaigne and Shakespeare to Dryden and Bossuet.