The order includes 30 A320neos and 14 A320s, Minister of State for Foreign Trade Pierre Lellouche said late Thursday as he arrived in Mexico on an official visit.
"I am delighted with this success," he told AFP. "This is the first major sale of European aircraft to Mexico. This opens up a new vista for the French and European aviation industry."
The planes are being purchased by Volaris, a budget carrier that competes with Mexico's national airline Aeromexico on internal flights.
Lellouche declined to say how much the sale was worth, but aviation sources said it could amount to some four billion euros ($5 billion).
He said Airbus hoped to build on its success and compete when Aeromexico renews its fleet, currently equipped entirely by the US Boeing.
"The arrival of the new A320s is great news not only for Volaris and the environment... (but) also for all of our customers," Volaris CEO Enrique Beltranena said in a statement.
"The new airplanes will let us strengthen our low price strategy to benefit a larger number of Mexicans, while their fuel efficiency and reliability will allow our fleet, the youngest in the country, to be even more friendly to the Mexican skies."
Volaris currently operates 34 Airbus aircraft and has a backlog of 58, including the new order.
Lellouche's visit is the first by a member of the French government since President Nicolas Sarkozy came to Mexico in March 2009.
Lellouche was due to meet with Mexican economy minister Bruno Ferrari later Friday.