The Big One - S3-E16
Other mistake: Headmaster Charleston called Rory to discuss the speech contest. His secretary conferenced in Paris. When Headmaster Charleston hung up, the connection between Rory and Paris should have been severed. They were both connected to him, not to each other.
Chosen answer: Lorelai and Christopher get married impulsively in Paris but they get divorced shortly after returning home. I don't know the exact number of days or weeks but they definitely weren't married for more than a couple of months.