The plane maker is facing investigations around the world over alleged corruption at a time when many of its most senior executives have laid plans to depart or already exited. While Airbus has secured orders for jets that have lengthened its backlog for years, it and rival Boeing Co. face big production challenges—including tight supply lines—to deliver those planes.

Airbus on Friday confirmed Chief Executive Tom Enders wouldn’t seek an extension to his contract beyond April 2019. His No. 2, Chief Operating Officer Fabrice Brégier, who runs the commercial plane division that delivers most of Airbus’s revenue and profit, will leave in February.