Langdon's got it figured out: he's holding the Priory keystone.
…and according to Priory lore, the keystone is an encoded map that reveals the hiding place of the Grail.
He gives an incredulous Sophie a lesson on the legend of the keystone.
Basically, the location of the Grail was passed down via word of mouth for centuries, until the last few decades when Priory policy changed.
Now it's never spoken aloud, but revealed via a series of tests. So, if you can open the keystone, then you deserve to know where the Grail is.
Sophie reveals that she thinks her grandfather was the Grand Master of the Priory. Langdon thinks it over, and realizes it might just make sense.
If that were the case, though, then he's flummoxed as to why the Grand Master would have requested a meeting with him, and why did he give the keystone to his granddaughter instead of one of the other three sénéchaux?
Langdon doesn't have time to figure it out. The truck comes to a stop earlier than expected.
When Vernet opens the doors, he's holding them at gunpoint.