If you believe FR24 data the aircraft was at 0ft before returning to the air. Check the CSV file and the timestamps. Would imagine this is fairly reliable ADSB data for this area.
Whatever happened the EFCS was probably in transition or transitioned to ground mode once it touched down as per design.
Once in this mode sidestick input and control output is essentially direct.
During the climb out the flight controls progressively returned to normal law and probably helped null out the oscillation.
As such, doubt anything was wrong with the aircraft, just a reactive input at the wrong time in response to an external event which led to the fairly dramatic oscillation seen.
The fact that the aircraft re-positioned to London after only 5 or so hours would suggest that whatever happened it wasn't a major fault as well. As if it was downloading flight data, analyzing it and discussing possibly with Airbus would take much longer that.
Out of curiosity and not to be picky whats the talk of an FCC on an A320 series aircraft? The EFCS main LRUs are ELACs/SECs/FACs/FCDCs and they all have specific functions within the overall EFCS.