Malaysia's low-cost carrier AirAsia is buying 200 of the A320neo jets, in a deal worth about $18bn (?11bn).
That eclipsed a deal on Wednesday, when India's IndiGo confirmed an order for 180 planes from Airbus.
The new versions of the A320 are in demand as their new engines make them more fuel-efficient and cheaper to run.
The AirAsia deal, worth about $15.6bn, is for 150 A320neos and 30 A320s. It is confirmation of a memorandum of understanding the two companies signed in January this year.
'Historic deal'Airbus said that the AirAsia deal made the Malaysian carrier its biggest airline customer for its single-aisle product line.
Altogether, AirAsia has now placed firm orders for 375 aircraft from the A320 family, with 89 already in service.
"With this historic deal, AirAsia has secured its future with the ability to meet the huge growth potential offered by the Asian market," said Tony Fernandes, chief executive of AirAsia.
Airbus, owned by EADS, has left rival Boeing far behind in terms of orders at the event, as high fuel costs increase the demand for more fuel-efficient aircraft.
Continue reading the main storyThough slightly modified, the 150-seat passenger jet itself is not new. But its engines are - and they are much better than anything else currently on offer”End Quote
Jorn Madslien Business reporter, BBC News, Paris air show It has taken firm orders for 586 aircraft, worth about $55.8bn, with a further $29.5bn in provisional orders.Boeing, meanwhile, has taken firm orders for just 47 planes, worth $7.5bn, with another $14.9bn placed in provisional orders.
Other manufacturers have also been signing contracts with airlines at the show.
Canada's Bombardier has received firm orders for 36 planes, with options for airlines to buy up to 26 more.
Russian-Italian joint venture Superjet International has signed a provisional deal to sell 12 Superjet 100 airliners to Italian carrier Blue Panorama Airlines for $370m.
The company, jointly-owned by Russia's Sukhoi and a unit of Italy's Finmeccanica, has 170 firm orders to date and delivered its first aircraft earlier this year.
Boeing's dilemmaAirbus estimates it has sold more than 700 A320neo jets so far.
Continue reading the main story Slightly modified version of the A320, with "sharklet" wing tipsSingle-aisle passenger jet, seats 15015% more fuel-efficient than the conventional A320, which should save airlines almost $1m (?625,000) per year per planeShould reduce CO2 emissions from each aircraft by 3,600 tonnes per yearSource: Airbus
"There is a possibility that we will be at 1,000 by the end of the show," said Airbus sales chief John Leahy.According to the BBC's aerospace industry specialist, Jorn Madslien, the A320neos are proving popular because their two new engines are 15% more fuel efficient and 30% cheaper to maintain than current models.
But Airbus' success leaves Boeing with a very tough dilemma, our correspondent at the air show says.
The US planemaker's A320 rival is the 737, but the plane is very low, so fitting modern, fuel-efficient engines under its wings would be a tight squeeze.
Making it happen would require a new undercarriage, which is costly and difficult, as well as time-consuming, he says.
The airline's managing director Jeh Wadia said GoAir may take 15 planes each year Indian budget airline GoAir has ordered 72 new A320 Airbus aircraft in a deal worth about $6.1bn (?3.7bn) at list prices.