The aircraft, MSN95, and the first long-haul Airbus for the UK carrier, is due to be delivered to BA in July.
BA says the Rolls-Royce Trent 900-powered aircraft has had its 469-seat cabin installed and will be flown to Toulouse for final checks before handover.
Its livery includes some 10,000 individual dots on the tailfin to produce the effect of the Union flag.