In general, the exorbitant wealth of the Medici kept Florence among the major players. With the cash they had, they could hire all the mercenaries they needed, though Machiavelli, while he held office, insisted on training a loyal citizen militia. In the 15th century, the Medici never officially held office, but they were the most powerful of the noble families, and therefore the de facto lords of the city. Their power waned around the turn of the 16th century, when they were exiled. The Florentine Republic coincides with Charles V's invasion, and whether any of the Italian states can be said to have kept their independence from the French in this period is up for debate. In 1512 the Medici returned and held the city thereafter. In 1530, they were granted a hereditary dukedom, making them the official lords of Florence.

Oh, and in 1513, Giovanni de' Medici was crowned Pope Leo X, which certainly didn't hurt.