Chief Executive Officer Frederic Gagey said the four-day walkout over pay curbs would cost the airline about 5 million euros (£3.83 million) each day.
"Of course, we'll look after the Euro tournament," Gagey told a news conference.
The strike was called by unions Syndicat National des Pilotes de Ligne (SNPL), which represents more than half of the airline's pilots, and SPAF, which represents about a quarter, after marathon negotiations this week collapsed.
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Air France, part of Franco-Dutch group, said about 25 percent of its pilots would strike, while the largest union in the country said one in two pilots would not show up.
Last week Gagey suggested a tough stance on the strike even if it meant disruption to the Euro tournament, telling reporters at a global airlines meeting in Dublin that fans stranded by the strike could "drive or take the train," or else fly on Dutch sister airline KLM or U.S. partner Delta.
The pilots strike comes amid weeks of nationwide protests against plans to loosen France's strict labour laws, which have blocked refineries, disrupted rail travel and left garbage piling up on the streets of Paris.
(Reporting by Cyril Altmeyer, Tim Hepher; Writing by Richard Lough; Editing by Laurence Frost and David Evans)
