Both Airbus and Boeing also marked leasing deals with EgyptAir on a record-breaking day for the show.
Indigo Partners' airlines have placed previous orders for a total of 427 Airbus A320-family aircraft.
"Hopefully I can do better than that", he added.
The stunning magnitude of the deal - which Airbus called its "largest single commercial announcement ever" - caught many in the aviation industry by surprise.
Franke did not take part in a signing by airline chiefs.
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After final purchase deals with each are confirmed, likely by the end of the year, Hungary's Wiz Air will receive 72 A320neos and 74 A321neos, USA carrier Frontier Airlines will receive 100 A320neos and 34 A321neos, Chile's JetSMART will receive 56 A320neos and 14 A321neos and Mexico's Volaris will receive 46 A320neos and 34 A321neos. Dubai is geographically at the centre of the global aviation world, and Dubai Airshow is where the sector comes to do business.
Franke went to Airbus several months ago with a proposal to pool the needs of his airlines, setting in train a complex negotiation that one observer described as "herding cats".
FlyDubai, which is like Emirates owned by the Dubai government, hit the news on Wednesday when its chairman Sheikh Ahmed Bin Saeed Al-Maktoum said the low-budget carrier would buy 225 aircraft of Boeing's 737 MAX family for 27 billion dollars, the largest-ever single-aisle aircraft order, in terms of number of units and airplanes.
Airbus, shares of which rose by 2.4 per cent on Wednesday, said it expects to finalise the transaction directly with the airlines in the coming weeks as it tries to close a 250-plane deficit in its order race with Boeing. The third Airbus deal involved 15 Airbus 320neo was announced at the air show by AerCap Holdings and Egyptair.
The deal marks a major coup for Airbus's Chief Operating Officer John Leahy, who is expected to leave the group soon at the end of a career in which he oversaw the sale of almost 15,000 planes. The two rivals account for the vast majority of the market.