Clearly nothing to do with the battery in the key fob since the driver's door unlocks with the key.
The usual system is for the driver's door mechanism to trigger the locking of the other doors electrically, so a fuse would allow the driver's door to unlock but the other doors wouldn't. There could also be an elecrical problem with the mechanism on the driver's door - water ingress causing a corroded connection/broken wire/swich burnt out etc. The fuse is the place to start and then take the lining off the driver's door and check the mechanism there.