A319 Captain reported the failure of ELAC2 in flight and discovered that it was only re-settable on the ground. The Captain elected to continue to destination airport and entered the discrepancy in the aircraft log book.

Narrative

While in cruise flight at FL390; we experienced an uncommanded altitude climb. The auto pilot was engaged at the time. There was no master caution or warning alert. The aircraft felt as if it were kicked and pitched up abruptly. I immediately disconnected the autopilot stating my aircraft. A review of the ECAM revealed ELAC 2 fault. My First Officer had indicated when he arrived to the flight that he was relatively new to the Airbus. I elected in this regard to have him do the ECAM procedure rather than attempt to hand fly at FL390. The flow indicated reset but had the words ON THE GROUND ONLY. No reset was attempted. We notified Dispatch via ACARS and the station upon landing that there was a write up in the book. Dispatch replied with a question of if it were one or both ELACs. The flight attendants all said they felt the kick I mentioned earlier in this report. They also indicated that several passengers expressed concerns. The auto pilot was re engaged and the aircraft was flown into ZZZ without further incident. This was a case of a system malfunction thus no causal factors that I can think of exists.