Why is a part from a Boeing 777 being analysed by Airbus?
Why are they taking the wing to Toulouse, FR?


Because the part was found on the island of Réunion, which is French territory.


  Why is a part from a B777 being analysed by Airbus?


It is not. Airbus is not the only company/institution to have plants/facilities in Toulouse: The BEA (France's equivalent to the NTSB) also has facilities there.