Hi.
The specific problem with the B777 events is being addressed by a SB, which our fleet will complete mods by the end of this month. (We have a modest fleet of these aircraft, about 25 at present with about another 15 coming). the engagement logic will preclude the autopilot being engaged on takeoff until above 50'RA. Normal minimum engagement altitude is 200'RA, by the AFM limitations.
Your suggested causation is pretty good, that any MCP modification post the flight control check, which is completed after engine start has the possibility of accidentally selecting the AP switch. The AP/FD mode will change and be annunciated correctly above the attitude display, and will have an attention getting box for 10 seconds following mode change, but could be missed in practice. For the AF case, the possibility is that the failure of the TOGA switches to engage the Auto throttle resulted from not arming the ATR switches (L&R) on the top LHS of the MCP, and proximate to the Captains side AP engage switch (2 fitted, one at each end of the MCP) Various actions could be taken by a flight crew member that may place their hands near the AP switch, more likely on taxi or on a takeoff if human nature exceeds SOP's.
A flight control check prior to takeoff would identify an engaged AP, as would the annunciation on the PFD, and of somewhat less value, the lit up lower section of the switch.
On the B777, the handling pilot would be confronted with a control system that appears jammed in roll and pitch channels, as the AP back drives through the flight controls.
The failure to observe an annunciation change is not uncommon, and there are few clues other than a control check that would otherwise indicate an inadvertent engagement.
On a normal takeoff, there is little input in the elevator channel or ailerons unless there is a very light weight takeoff, slippery runways, or crosswind condition.
AFAIK, the ground engagement has been operator related not a failure of the system such as internal shorting of the Korry switches. It may be that this is not the case..... that would be a surprise.
Control checks are like flossing, only floss those you want to keep.
The control check changes on the Airbus were for a different reason, but do appear prudent, as would a rigorous review of modes selection prior to takeoff. Any such procedure relies on human performance, so there is room for failure.
regards,
FDR