The airline said it expected to cancel up to 35 percent of long-haul flights and up to 25 percent of shorter flights during the day.
Extra costs included compensating passengers, rebookings and notifying thousands of passengers of axed flights this week via email or text message, the spokeswoman said.
The strike has added to travel disruption caused by freezing temperatures across Europe.
The SNPL pilots' union said around half its members were taking part in the action over plans by the government to make strikers in the airline industry give two days' notice before any walkout, rather than no notice.
Transport minister Thierry Mariani said earlier this week the government was determined to push through the legislation, which would let airlines plan minimum services during a strike rather than waiting until the strike day to find out how many staff were coming to work.
The legislation, adopted in the lower house of parliament in January, will be taken up by the Senate in mid-February.
Air France (AIRF.PA) shares were up 2.4 percent at 0940 GMT.
(Reporting by John Irish and James Regan; Editing by Dan Lalor)
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