Danone SA (DANOY) shares rose sharply again Tuesday following reports that an activist investor has built a stake in one of the world's biggest yogurt makers.

Danone was marked 1.9% higher by mid-day in Paris to change hands at €67.70 after Bloomberg reported that Corvex Management, a U.S.-based fund controlled by Keith Meister, has taken a €400 million stake in the French group and wants to press for changes from the company's management that he argues would unlock value in the group.

Danone shares were also active in Monday's European session after the New York Post reported that the group could be a potential takeover target, although some analysts questioned the ability of a U.S.-based takeover given the French government's previous reluctance to allow foreign ownership of what it has called a "flower of our industry". 

The shares have gained 2.5% over the past two days and 7.8% so far this month, far outpacing the 1.02% gain for the benchmark CAC-40.

The French government has consistently thwarted foreign investment in the daily industry, which generates nearly €30 billion in annual revenue and employs more than 250,000 people in Europe's second largest economy.

In 2011, French private equity group PAI was essentially forced to split its holding in Yoplait, a yogurt maker, into a brand unit and an operating unit before it could be sold to U.S.-based General Mills Inc. (GIS - Get Report) in a deal that was wroth around $2.3 billion at the time.

General Mills and Sodiaal, a French farmers' co-operative group, took equal ownership of the brand company while General Mills took 51% of the operating group.

"The government reaffirms its desire to preserve jobs and the future of the dairy sector in France," said Christine Lagarde, now Managing Director of the International Monetary Fund but then France's Finance Minister. "It will be particularly keen to see the shareholders put forward an industrial plan that favours job creation, innovation and milk producers."

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