Airbuses do not does not takeoff with autopilot on, just flight director.
On the airbus the common modes for takeoff are Lateral : RWY (Runway) and Vertical/Speed : SRS (Speed Reference System).
The SRS give you V2+10 in normal config, or the greater of current speed/V2 OEI configuration to the acceleration altitude, with a maximum pitch of 18 degrees, and minimum V/S of 120 ft/sec.
The flight director is available on the takeoff run and initial climb, the autopilot engages 5 seconds after takeoff. This relies on a localizer being available, being 1/2 dot on the localizer, and heading with 20 degrees of the ILS course.
The primary flight display in this mode will show a yaw bar so you can tell the effect of wind.
If you not set this up, the aircraft will maintain runway track (RWY TRK) at 30 ft rad alt if you forgot to arm the nav mode before takeoff.
Royans comments above are airbus specific.