I took it to the Ford dealer, and they said it was a "door ajar switch". Problem is, the only door ajar switches are located in the sliding doors.
The front door sensors are integrated into the door latch / lock system, so they're no individually replaceable.
It seems hard to believe that a faulty switch on one of the sliding doors could be "set off" by opening the right - front passenger door, but I guess anything is possible.
I'm going to try replacing one or both of the sliding door switches and see if that fixes the issue.