"The situation is improving," according to the Directorate-General for Civil Aviation (DGAC).
French authorities have asked airlines to reduce their flights today by 15%, compared with the 40% reduction requested on Sunday.
"Despite these preventive measures, delays are expected," the authority said in the statement.
DGAC did not provide details on the cause of the failure.
The French airport's air traffic control systems registered a failure on Sunday, which had not yet been resolved by evening, causing around 130 flights to be cancelled, half on departure and half on arrival, that is, around 40% of the 330 scheduled flights.
Paris-Orly Airport serves domestic and international flights, including to most European countries and the United States.
More than 33 million passengers passed through Paris-Orly airport last year, about half the number at Paris-Charles-de-Gaulle, according to figures released by operator Aeroport de Paris.
In August, a failure disrupted the baggage handling system at Paris-Orly Terminal 4 for more than 12 hours. The "unprecedented" outage affected around 10,000 passengers in the middle of the summer peak season, causing delays in departures and forcing airlines to operate flights without checked baggage.