While the headquarters of Airbus is in France (Toulouse), the components of a plane are manufacturered in different countries in Europe, mainly UK, Germany, France, Spain, etc. The components will be shipped to France for assembling.
Airbus itself is not an airlines... Airbus itself is a aircraft manufactory base in Toulouse and have factories across Europe... Although Airbus is not an airlines but it do have airlines IATA/ICAO code allocated to them which are XL/AIB...
This is mainly because Airbus is required to operate flights to shuttle parts between their factories across Europe using their A300ST... And these flights will carry Airbus IATA/ICAO code and operate with Airbus livery...
Beside that, Airbus is also required to operate test flights before a new aircraft is being delivered to airlines for revenue operation... And these IATA/ICAO code will also be used at these situation although now the livery will be the airlines which will be taking delivery of the jet...