1 of them is the AC radiator fan, the electric fan on the front of the car which you can see on the left inside side of the radiator. If it is unplugged the fan will not work and likely the AC gas will overheat, you may be ok if travelling fast but in slow traffic this would not allow enough cooling. What would happen if it overheated? - fuse blow/safety cut out/ac gas overpressure & escape somewhere? I would guess any of these would cause the AC system not to work and therefore not allow the econ button to be turned off.
The other connector also goes to something in the front end carrier as I had to unplug both this weekend to remove the front end to do the timing belts - has something like this been done recently and forgotten to be reconnected?