The film shows 50-year old Lagardère and his Belgian girlfriend of six months, model Jade Foret, in a range of suggestive poses while they are photographed.
The video was made by top-selling Belgian newspaper Le Soir, which interviewed the couple for its magazine. The 20-year old Foret is a well-known model and TV presenter in her home country.
After a short interview at the start of the three-minute video, the couple are shown posing suggestively in a variety of outfits and positions with the accompaniment of an ambient music track.
In some scenes, the statuesque Foret is shown towering over her more diminutive partner, aided by the thigh-high stiletto boots she is wearing.
The couple are then seen lying on a chaise longue gazing lovingly at each other, the model's breasts barely covered while he caresses her legs.
In a short interview at the start of the video Lagardère explains that they are doing the interview "to show we're together and we're serious." He adds that they met in Paris but the relationship got going in London.
Lagardère is boss of a huge media empire that includes Paris Match, Journal du Dimanche and Europe 1 as well as a leading publishing business. The group's interests also include a stake in aircraft manufacturer EADS.
Daily newspaper Liberation sought the views of some of Lagardère's employees. The responses were not particularly positive. One commented,"what's sad is that he looks like a baby in this video", while another said, "this says a lot about him, as if he hasn't finished growing up yet."