The video, which provoked much mirth in France, showed 50-year-old Arnaud Lagardère striking a series of provocative poses with Jade Foret, a well-known Belgian model and TV presenter. An ambient music track in the background completed the mood.
The film was shot as the two were being photographed for top-selling Belgian newspaper Le Soir.
In the interview on Tuesday with French business daily Les Echos, Lagardère said he wouldn't be caught out again.
"When you have a camera in front of you that's filming you while you're being photographed, it's difficult to say you've been trapped," he said. "If I'd known it would be distributed in the way it was, I wouldn't have accepted"
Despite the embarrassing film, which Jade Foret herself described as "kitsch", the two are still an item.
"As for my relationship with my fiancée," he said, "I'm really happy about it."
Lagardère heads up a huge media, publishing and retail empire that also has a stake in aircraft manufacturer EADS, which it plans to sell. The company was founded by his father, Jean-Luc, who died in 2003.
In the interview he rejected claims that he has not been sufficiently devoted to the business.
"I have lived with and for my group since I was tiny," he said. "I've personally invested everything I have in this business. To accuse me of being someone who hasn't invested enough in this company or who doesn't spend enough time on it … that's like the video: ridiculous!"
Lagardère was nevertheless prepared to accept that he is, perhaps, an unusual type of business leader.
"Perhaps I am an atypical boss, different," he said. "Big deal!"