British citizen Mae, who has sold several million albums of her self-described "violin techno-acoustic fusion" music, skied for Thailand at the Games under her father's surname of Vanakorn.
She was given the ban in November when FIS listed a series of irregularities at four qualifying races at Krvavec, Slovenia, and her Sochi results were scrubbed.
The issues cited included competitors who had not taken part, and races staged in irregular weather conditions. The results gave Mae the number of FIS points necessary to be able to compete in Sochi.
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The 35-year-old finished last among the finishers in her race at the Winter Olympics, some 50 seconds behind gold medal winner Tina Maze -- an eternity in the world of downhill skiing.
CAS said in a statement on Thursday that it had received two appeals from Mae, filed against the International Ski Federation decision to ban her.
Countries which did not have a skier ranked among the world's top 500 were allowed to send one male and one female skier to the Winter Olympics if they met a sufficiently high standard.
She had tried to enter for Thailand at the 2002 Winter Olympics but at that stage the country had wanted her to give up her British passport in order to do so.
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