Thwarted by Sir Martin Sorrell's WPP in its bid for Grey Global Group, Havas is being mooted as a takeover target itself after Bollore upped his stake in the company to more than 10 per cent last week.
Although Bollore has ruled out a bid at this stage, his pledge to buy more shares is expected to intensify the pressure on Alain de Pouzilhac, the Havas chairman.
He could be urged to step down in the wake of the abortive Grey bid, which Bollore opposed as too risky, and Havas' recent lacklustre financial performance.
Speaking to the French daily newspaper Les Echos this week, Bollore, 54, confirmed he would be asking for several seats on the Havas board.
De Pouzilhac has indicated that Bollore could have two board seats and claimed that having him as a core shareholder would give the company stability.
Pierre Dauzier, a former Havas chairman, who is close to Bollore, could be appointed to head a new supervisory board.
Onlookers say Bollore's action is in line with his strategy of taking stakes in weak companies and then advocating a restructure or taking capital gains on shares that often rise in value on the news he has bought them. Bollore is already sitting on a profit of more than £7 million.
Under French stock market rules, a company must state its intentions once it has bought more than 10 per cent of another operation.
Bob Willott, the editor of Marketing Services Financial Intelligence, said: "Maybe Bollore thinks Havas can either be broken up or sold to a big player."