The king of France -- Philip IV wanted the Templar's money. Philip pushed his captive Popes (just as Henry 8 etc. could push their captive Archbishops) to comply to his wishes. The Pope's didn't "team up" rather were coerced by a powerful king who had already moved them out of Rome to under his thumb in Avignon.
Furthermore, even after this Pope John XXII, the successor to the above Clement V was the one who allowed the reconstitution of the Templars (btw, the Templars STILL exist as a Catholic order) as the Order of Christ in Portugal.
The freemasons aren't derived from them, any more than whoever believes this would believe Dan Brown that Jesus got married and had kids...
Just to clarify,
“The Militia Templi is a Roman Catholic private association of the faithful that celebrates its liturgy according to the traditional form in place in 1962, often referred to as the Tridentine Mass.
“Founded by the Italian Count Marcello Alberto Cristofani della Magione under the authority of the Roman Catholic Archdiocese of Siena-Colle di Val d’Elsa-Montalcino, the Militia Templi’s focus is knightly and monastic and members follow a modern adaptation of the Rule written by St. Bernard of Clairvaux for the medieval Knights Templar. The order makes no claims of direct descent from the old Knights Templar and holds that, when made, such self-styled claims are both historically and canonically false.”
They are more like a revivalist group, than a direct offshoot from them. More info:
http://en.wikipedia.org/wiki/Militia_Templi.
I have to say I find them appealing. But that’s because I’m the chivalric type.
-Theo