Xavier Niel, an entrepreneur who shook up the French mobile market in 2012 with the introduction of Free, a low-cost mobile service, is also supporting Mr. Bouygues's bid, though Mr. Niel's service has damaged the profit margins of the other three players and is a major reason for the current turmoil in the mobile market.
Bouygues Telecom agreed last month to sell Mr. Niel portions of its existing mobile network's hardware and a number of valuable radio frequencies for 1.8 billion euros ($2.5 billion), if the deal goes through, to address antitrust concerns. That side deal would transform Mr. Niel into a much more important telecom player in France.
Both Mr. Bouygues and Mr. Drahi declined to comment.
Vivendi also declined to comment, beyond saying that it planned "to work in the best interest of our shareholders and employees."
The focus on choosing between the billionaires is misplaced, according to consumer advocacy groups. Antoine Autier, a project manager at UFC-Que Choisir, France's largest consumer organization, said the government was not paying enough attention to the concerns of mobile phone users.
"There's a certain incoherence in the government's thinking," Mr. Autier said. On the one hand, "they're saying the market needs to shrink because four operators is too many," he said. "On the other, they're saying prices are not going to rise for consumers."
French mobile rates, once among the highest in Europe, are now among the lowest, thanks to Mr. Niel's Free mobile service, Mr. Autier said. "Competition has been very beneficial for the consumer," he said.
The open involvement of the French government in trying to shape the outcome of battles between big businesses traces back to the famous 17th-century finance minister Jean-Baptiste Colbert, a strong believer in the state's role in the creation of wealth.
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Acceptance of Colbertism, which contrasts with Adam Smith's "invisible hand," is shared to some extent across the French political spectrum. Jacques Chirac's center-right government in 2005 stopped a takeover of Danone, the French yogurt maker, by the American giant Pepsi. More recently, Mr. Montebourg blocked a plan by Yahoo — another foreign company — to acquire Dailymotion, a French competitor to YouTube.
In those cases, the government was worried that strategic assets would be sold to foreign companies that were not focused on maintaining French jobs. But the current case involves two French investors.
Speaking in a radio interview last month in which he clearly signaled his preference for Mr. Bouygues's plan, Mr. Montebourg raised concerns about Mr. Drahi's personal finances.
"Numericable is a Luxembourg holding, his company is quoted on the Amsterdam bourse, its boss's personal holding is in Guernsey, a tax haven of Her Majesty the Queen of England, and he is a Swiss resident," Mr. Montebourg said. Should he return to France, Mr. Montebourg added, the tax authorities "will have some questions for him."
Mr. Montebourg appeared to be backpedaling this week, saying Tuesday on France Inter radio that "I don't support Bouygues, I don't support anyone, and I have no friends in the grande bourgeoisie française."
Nonetheless, Mr. Boulan of Nomura said that Mr. Montebourg's promotion to economy minister had added a new element to the equation because that would theoretically give him the authority to overrule French antitrust regulators.
Whatever happens, consumers will be watching their phone bills closely.
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