BA and Ryanair have cancelled flights on Wednesday and Thursday as French traffic controllers start their fourteenth bout of industrial action this year.
Ryanair cancelled 22 flights on Wednesday night and 72 on Thursday.
Aer Lingus also said a number of flights have been cancelled.
Flights that normally route through French air space are affected. Passengers are advised to check the status of their flights.
BA declined to say how many flights had been affected, saying the information goes out of date quickly.
BA said: "Unfortunately, if the threatened strike does go ahead, we will have to cancel some flights, and other short haul flights may also experience some delays and disruption, given how many flights would normally use French airspace each day."
It said it would use larger aircraft, where possible, to help affected customers.
Ryanair warned there could be more delays.
Ryanair said: "This French... strike will impact hundreds of thousands of European consumers and throw their travel plans into chaos once more.
"It's high time that the European Commission takes action to prevent these repeated... strikes from continuously disrupting the travel plans of millions of Europe's citizens and their families."
BA has offered customers due to fly to or from France on Thursday the opportunity to rebook.
The lobby group Airlines for Europe (A4E), which represents airlines including EasyJet, Ryanair and BA's parent company IAG, has called on the European Commission and governments to take action to reduce the impact of air traffic control strikes.