While the list price of the aircraft is $49.5 billion, Airbus confirmed that "regretfully" the private equity firm did not pay that price, with the final cost not being revealed.
Franke added that the deal will be on a sale and lease-back basis and he will now seek financing before proceeding with the order.
The industry veteran added that he foresaw no problem securing the deal and that he was hopeful a firm contract order could be resolved by the end of this year.
The deal puts an emphatic full stop on the career of Airbus sales chief John Leahy who is set to retire after more than 20 years as the firm's marketing boss.
During the announcement Leahy said the "incredible" bulk order for 430 aircraft would not affect Airbus's current production rate.
"It's particularly gratifying to all of us at Airbus when it comes from a group of airline professionals who know our products as well as the folks at Indigo Partners do. We are proud to augment their airline fleets," he said in a statement.