Shares in the company were down by 22% on the news, trading at €4.52 at the time of writing, although the price dipped as low as €4.49 during the day.
Dru had been seen having discussions with Omnicom boss John Wren during last week's Cannes advertising festival. He was widely seen as a good choice to take on the chief executive role at Havas because of his success in running the TBWA\Worldwide network and because of his status as a high-profile, well-respected Frenchman.
However, TBWA has now put an end to the speculation that Dru will take over after De Pouzilhac's departure -- which was sparked by his failure to prevent the French businessman Vincent Bollore from taking four seats on the board.
In an interview with the French newspaper Le Monde, Dru said: "My place remains as the head of TBWA."
No other suitable candidates have been mentioned for the role, which was vacated by De Pouzilhac during a board meeting last week, and Bollore, the largest shareholder in Havas, had supported Dru taking on the role.
De Pouzilhac, 60, will remain a Havas board member until June next year and will continue managing accounts such as Peugeot, with which he has a long relationship.
In the absence of a chief executive, Havas is being run by board member Richard Colker, who has taken on the position of interim chairman chief executive with the support of Havas executives.
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