From the Wikipedia entry on the 'Avignon Papcy,' aka the Babylonian Captivity:
Following the strife between Boniface VIII and Philip IV of France, and the death of his successor Benedict XI after only eight months in office, a deadlocked conclave finally elected Clement V, a Frenchman, as Pope in 1305. Clement declined to move to Rome, remaining in France, and in 1309 moved his court to the papal enclave at Avignon, where it remained for the next 67 years. This absence from Rome is sometimes referred to as the "Babylonian Captivity of the Papacy". A total of seven popes reigned at Avignon; all were French, and they increasingly fell under the influence of the French Crown. Finally, on September 13, 1376, Gregory XI abandoned Avignon and moved his court to Rome (arriving on January 17, 1377), officially ending the Avignon Papacy.
- Clement V stayed put - probably out of fear for his saftey
- France saw fit to keep it that way