Schmetterer, 60, is stepping down as the chairman of the Havas-owned Euro RSCG Worldwide network to be succeeded by the former McCann-Erickson chief, Jim Heekin.
The rumours come at the worst possible time for Havas. It wants to present Heekin's appointment as a positive signal to the investment community that it is taking action to address its problems in advance of what is expected to be a less-than-impressive set of results in March.
As speculation swept through the financial markets on Wednesday morning, Havas issued a statement denying "unfounded rumours" of alleged accounting irregularities and said it had called on French regulatory authorities to launch an immediate investigation into the possible manipulation of its share price.
The company's shares rallied after the announcement. Jacques Herail, the Havas financial director, said: "Rumours that Ernst & Young would not certify our accounts are absolutely unfounded. Audits are under way on the close of our accounts and are proceeding smoothly."
Schmetterer, who was seen by some as a potential successor to Alain de Pouzilhac, the Havas chief executive, insisted he had made up his mind to quit over Christmas. "My decision to retire from advertising is not a sudden one," he said.
Heekin was appointed president and chief operating officer of Euro RSCG in September last year, six months after being ousted from McCann, where he had been made to pay the price for a disappointing performance. Heekin was enraged by his sacking and complained that he had been made a "fall guy". But de Pouzilhac said: "I have great confidence in Jim."
Industry analysts were not surprised by the drop in the Havas share price, which they blamed on market jitters ahead of its results.
"It may well be that the market has over-reacted," Bob Willott, the editor of Marketing Services Financial Intelligence, said.
"Havas has clearly concluded that it's losing ground and wants Heekin's appointment to be interpreted as a sign that action is being taken. There are unanswered questions about Heekin's time at McCann but he has a good reputation as a business builder in the US and Europe."