Agnes Saal found herself at the centre of controversy this week when Le Figaro daily revealed her exorbitant spending on cabs.
The scandal was compounded by the fact her son was allegedly responsible for 6,700 euros (USD 7,350) of the 40,000 euros in taxi rides.
Culture Minister Fleur Pellerin asked Saal, 57, to resign with immediate effect, the ministry said today.
Saal had been head since April last year of France's National Audiovisual Institute, a public body that preserves and promotes the country's radio and TV heritage.
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Anti-corruption association Anticor had threatened to go to court if Saal did not step down.
"It's about public money and significant amounts of money," Anticor head Jean-Christophe Picard told Le Parisien daily today.
"Anyone with rudiments of accounting would start at such sums.