His company Bollore Group has written to Aegis, owner of the media buying agencies Carat and Vizeum, ahead of its annual general meeting, to be held on May 23.
Shareholders will be asked to vote on whether Philippe Germond and Roger Hatchuel should be appointed as directors of Aegis.
Shareholders have been asked to vote on the same matter four times in the past, since Bollore began buying up shares in Aegis in 2006, but have rejected the request every time by more than 90% of shareholders.
Bollore argues that he should have representation, as the biggest single shareholder in the company with a 29.9% stake.
However, Aegis directors, including chief executive Robert Lerwill, have argued that it is bad corporate governance to have the chairman of a rival on the board, as well as bad for competition.
The company, which also owns market research network Synovate, will also be writing to shareholders in due course.