This period ended immediately after the War of the Eight Saints.
The man who started this period of time had just burned Fra Dolcino at the stake. It came to an end shortly after a man employed Sir John Hawkwood to wage a war before he excommunicated the entirety of Florence. This period ended immediately after the War of the Eight Saints. The man who ended this time period did so after reading a letter written by Catherine of Siena. Right after this period of time began, Jacques de Molay was burned at the stake and the Knights Templar were effectively dissolved. Gregory IX's decision to end this period of time prompted Clement VII to become antipope, kicking off the Western Schism. For 10 points, name this time period when the papacy was ruled from a namesake French town.
The man who started this period of time had just burned Fra Dolcino at the stake.
Avignon papacy [prompt on Babylonian Captivity, a Petrarchan euphemism, do not accept antipapacy or Western Schism as the tossup doesn't talk about them]