A spokesman for Aéroports de Paris, which operates the French capital's second busiest airport, said on Sunday about 40 percent of the day's departures and arrivals had been called off.
France's DGAC civil aviation authority blamed "a failure of the air traffic control systems at the Orly tower early in the afternoon" for what it said had been a "significant" reduction in the number of flights.
The DGAC has asked airlines to cancel 15 percent of scheduled flights from Orly on Monday.
It is up to airlines to decide which flights to cancel, and they usually try to prioritise long-haul flights - anyone with a flight booked for Monday should contact their airline.
The disruption remains specific to Orly airport, and Paris' Charles de Gaulle airport is running as normal.
An aviation source told AFP that a radar breakdown caused the airport chaos.
The airport spokesman said about half the 130 flights cancelled on Sunday were departures and half incoming flights.
Flights across France and to other European destinations and North Africa were among those hit.
Stood near a line of suitcases, Agnes Zilouri, 46, tried desperately to find a seat for her 86-year-old mother and six year old son. The family had been meant to take a flight to Oujda in Morocco on Sunday evening to go to a funeral.
"The flight is cancelled. Fortunately I am with my mother," she said.
Last year Orly handled about 33 million passengers, approximately half the number of the main Paris Charles de Gaulle international airport.
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