The war of words comes ahead of Thursday's crucial boardroom vote when the future of Havas could be decided.
Bollore, who owns just over 20% of Havas, is pushing for four seats on the board, but De Pouzilhac is seeking to thwart his ambitions.
In interview in French daily Les Echos, De Pouzilhac said that Bollore had shown a "lack of loyalty" by opposing Havas in its attempts to acquire Grey Global Group.
Bollore had voiced his disapproval for Havas' takeover bid for Grey, which eventually went to Sir Martin Sorrell's WPP Group. It later emerged that Sorrell and Bollore had been talking for as long as two years and had discussed the future of Havas together.
In the Les Echos interview, De Pouzilhac said that granting Bollore seats on the board will cause trouble.
"His arrival on the board would pose an enormous problem for this company," De Pouzilhac said.
He went on to warn shareholders of a risk of takeover on the cheap.
"Ther is a clear risk of a creeping takeover without a strategic plan and without paying the right price," he said.
Bollore is reported to have gathered at least 30% of Havas' voting rights, giving him considerable influence at Thursday's shareholders meeting.
De Pouzilhac has called on shareholders to reject Bollore's demands for seats, saying that Havas's management was "unanimously opposed" to the move and said it would destroy the company.
"To destroy confidence in a creative company is to destroy value," De Pouzilhac warned.
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