It's generally agreed that the charges were false. I think the best evidence for this is that the church tried and exonerated the Templars in many countries outside of France. It was only in France, where Philip the Fair had enough influence to force the outcome, that the Templars were convicted. The other major piece of evidence historians point to is that all of the confessions that were made while the Templars were being tortured were recanted once the torture stopped.

As to why the Templars were "turned on" so quickly...First, outside of France they weren't. In fact, people outside of France seemed horrified by the treatment of the Templars by the French king. Inside of France, the French monarchy had been gaining more and more power since Louis VI in the early twelfth century. By the time that Philip the Fair was king, in the early fourteenth, the French monarchy had considerable power inside France. Add to this that the papacy was at a low point and struggling for power with the French king. The church elected a French Pope, Clement, who ultimately didn't move to Rome, leading to the Avignon Papacy (aka the Babylonian Captivity of the Papacy). Although Clement doesn't seem to have willingly collaborated with Philip to destroy the Templars, he couldn't do much to protect them because he was inside France and therefore under Philip's control to a certain extent (the Popes in Rome were much more autonomous). Thus Philip was able to simultaneously attain his goals of wiping out the Templars in order to gain their wealth and of increasing his own power by wiping out a powerful part of the church (the Templar order) and usurping power from the Pope.

The major author on the Templars was Malcolm Barber. He wrote a history of the Order, The New Knighthood which is still a pretty standard text on them. He also wrote a deep overview of the trial, called The Trial of the Templars, which goes into an in depth discussion of the trial and its aftermath.