Cuche, 41, appeared in La Chaux-de-Fonds police court to deny any wrongdoing in the June 21st 2014 traffic incident when the car he was driving struck two striped road barrier posts.
The ski champion, who retired in 2012, told the court the accident happened when he swerved to avoid striking an animal as he drove home at around midnight after visiting friends at a barbecue party, Swiss media reported.
Cuche, a native of Neuchâtel who won world skiing titles in the downhill, super-G and giant slalom categories, said he had no more than two glasses of wine before driving home.
He failed to stay at the scene of the accident and only reported the crash to police several hours later when he left a message on the police telephone answering machine, the ATS news agency said.
Justice officials said he concealed damage done to his car and also violated safety regulations by driving a vehicle that was not in roadworthy condition.
But Cuche and his two lawyers denied that he was inebriated at the time of the accident.
They maintained he had not been driving at an excessive speed and the slight damage caused to his car allowed him to drive safely home, ATS said.
He said he lent his mobile phone to a person who was at the accident scene to allow the person to inform police, the news agency said.
One of his lawyers said that Cuche left the accident scene because he did not want to be the victim of a passerby who might have taken a photo of his damaged vehicle and circulated through social media.
“I know that these images would have ended up landing in the press,” Cuche told a press conference after his court appearance.
“I am very sensitive to these questions of images, that can quickly degenerate,” he said.
In addition to the fine, the Neuchâtel prosecutor imposed a penalty equivalent to payments of 1,000 francs a day for 30 days suspended for a period of two years.
“I have the impression of being in a bad film and that I am going to wake myself up,” Cuche, who lives in the village of Bugnenets, told the press conference, ATS said.
“I experience some terrible moments,” he said, stressing that he wanted to restore his honour.
“My image has always been important to me.”
Also potentially at risk is an advertising deal he has with car company Audi, among others.
The judge of the police court is set to deliver his verdict in the case at the end of September.