The announcement came after renewed negotiations on Tuesday.
A statement on the the SNCTA union's website read: "After a last round of negotiations the SNCTA union of air traffic controllers, the majority union in the profession, has lifted its strike notice for July 2nd and 3rd."
The strike had been set to cause major travel chaos across Europe with French aviation authorities preparing to ask airlines to cancel scores of flights.
The lifting of the strike notice was confirmed by France's aviation authorities DGAC.
The good news for travellers comes as budget airline Ryanair launched a petition calling on the EU to take away the right to strike for air traffic controllers.
(An air traffic controllers tower at the Roissy-Charles-de-Gaulle airport, Paris. Photo: AFP)
Ryanair says that when a million people have signed the petition, named Keep Europe's Skies Open, it will be presented to the European Commission and used to pressure authorities into action.
As it prepared to cancel dozens of flights if Thursday’s strike had gone ahead, Ryanair also proposed that controllers from around Europe should be able to step in when the French go on strike.
In that way control centres around Europe could take over French air space and limit the disruption to passengers.
Ryanair’s chief marketing officer, Kenny Jacobs, said: “It’s unacceptable that Europe’s consumers repeatedly have their holiday and travel plans disrupted or cancelled by the selfish actions of ATC unions every summer, who use strikes as a first weapon rather than a last resort."