In a separate statement posted by Lufthansa, Franz said he was leaving for "professional reasons."
"After a total of nearly 15 years in the Lufthansa Group, this was not an easy decision for me to make," he said. "This is a suitable time for a management handover."
Wolfgang Mayrhuber, chair of Lufthansa's supervisory board, said he regretted that Franz was leaving but has "trust that in the remaining months he will be able to bring his work for our company to a successful conclusion."
At Lufthansa, headquartered in Cologne, Germany, Franz has headed a global aviation group with some 117,000 personnel.
Roche Holding AG, the world's biggest manufacturer of cancer drugs, employs 82,000 people worldwide and says it had more than 8 billion Swiss francs ($8.7 billion) invested in research and development last year.