Hulot, a celebrity green activist who is one Macron's most popular ministers, appeared close to tears in a television interview as he denied the “shameful” rumours.
“It hurts, when it's wrongful and unfounded. Yesterday my children were in tears,” said the 62-year-old, describing the situation as “a nightmare”.
Questioned on BFMTV about accusations from “the grand-daughter of a famous politician” dating back to 1997, he acknowledged that the woman filed a complaint in 2008 but said the case was dismissed.
“I was questioned at my own request and investigators very quickly concluded that there was nothing suggesting the case should be followed up,” Hulot said.
Hulot was attempting to clear the air ahead of the publication of an investigation by a French magazine this week which has emerged as another cloud around the TV star who has faced a difficult start to his life as a politician.
He also denied suggestions that a former colleague had accused him of harassment.
Hulot climbs up a wind turbine by its engine. Photo: AFP
“The answer is no,” he said. “The worst thing is that she has already been questioned by some of your colleagues and she gave the same answer.”
He said he had not yet considered resigning, but added: “My family comes first, that's what will guide my decision.”
The rumours dogging Hulot emerged after Paris prosecutors reopened an investigation in late January into rape allegations against Budget Minister Gerald Darmanin.
A former call girl claims he pressured her into sex in 2009 in exchange for helping her clear her name in a legal dispute.
Darmanin's lawyers have accused her of a “crude attempt to harm” the minister's reputation and said he was suing her for slander.
Other ministers have rallied around Darmanin and on Thursday Prime Minister Edouard Philippe offered Hulot his support, saying there was “no reason to doubt his words”.
France, like other countries around the world, has seen an outpouring of allegations of sexual assault and harassment in the wake of the scandal engulfing Hollywood mogul Harvey Weinstein.
Having campaigned for environmental protection for three decades, Hulot was among several figures Macron brought in from outside politics to brighten his cabinet when he was elected in May.
He has regularly been reported to be on the brink of resigning, frustrated over multiple issues including a decision to delay France's commitment to cutting its reliance on nuclear energy to 50 percent until after 2025.
After filing a declaration of his assets in December as required by ministers, press reports highlighted how the eco-warrior owned nine motor-engined vehicles, including an SUV.