The order trumps last year's record order for 230 Boeing planes - also from Lion Air.
The planes will be made in France and will secure 5,000 jobs there, where the unemployment rate is high at about 10%.
Lion, now a major airline in Indonesia, started up just 13 years ago.
The two orders, once fulfilled, would put the airline in the world's top 10 by number of aircraft, although Lion Air is banned from flying within both the 27-nation European Union and the US. because of fears that its safety standards are not up to scratch.
Lion currently has just 92 Boeing planes, which fly mainly within Indonesia but also to Saudi Arabia.
It operates the low-cost aircraft carrier model and holds about a 45% market share in Indonesia, a country spread across around 6,000 inhabited islands with a population of 240 million people.
Indonesia air traffic is forecast to grow at 20% a year, and the country's economy is growing at about 6% a year.
French President Francois Hollande said the deal should act as a shop window for France's manufacturing abilities: "Airbus is a national and European pride, one of the pillars of our economy.
"The big Airbus contracts are an example for our economy, what it can do, what it must do."
The planes are all in the A320 family of planes and the first are due for delivery in 2014.
Airbus makes civilian craft for the aerospace and defence consortium EADS, which is owned by France, Germany and Spain.
The UK is also banking on fast growth in the civil aviation market.
The government announced  a £2bn investment in the UK aviation industry, with half being provided by itself and the other half by aerospace firms.
Business Secretary Vince Cable said the sector was substantial within the UK.
"Our aerospace sector already supports more than 3,000 companies and employs 230,000 people across the UK," he said. "The potential for growth is huge. By 2031 the civil aerospace market will be worth in excess of $4.5 trillion."
The European-owned planemaker Airbus has won a record order for 234 planes worth 18.4bn euros (£15.7bn, $24bn) from Indonesia's Lion Air.