* French state to keep about 33.6 pct of GDF Suez
* Sale to yield 1.56-1.79 billion euros (Adds proceeds of sale, bookrunners)
PARIS, June 24 France has agreed to sell a 3.1 percent stake in gas utility GDF Suez, and could sell as much as 3.6 percent in order to finance the acquisition of a state participation in engineering group Alstom, the government said on Tuesday.
The finance and economy ministries said in a joint statement the state, via public holding firm APE, had agreed to sell 75 million GDF Suez shares and has an overallotment option to sell as many as 86 million shares in an accelerated institutional placement.
Based on Tuesday's 20.81 euro closing price, the operation would yield the state between 1.56 and 1.79 billion euros.
The sale will leave the French state - lead shareholder in GDF Suez with 36.71 percent stake - with a residual stake of around 33.6 percent according to a source close to the deal. By law, The French State cannot reduce its stake below 33.3 percent. Publicly owned bank CDC owns another 1.9 percent.
"This sale is part of an active management of state holdings ... the proceeds could be used to finance the state's entry into the capital of Alstom," the statement said.
On Sunday, the French state secured an option to buy 20 percent of Alstom from its current top shareholder Bouygues , clearing the way for an agreed tie-up between Alstom and General Electric.
According to the terms of the placement seen by Reuters, the shares will be sold overnight in a price range of 20.18 to 20.81 euros, which represents a maximum discount of 3 percent on Tuesday's closing price. Citi, Bank of America Merrill Lynch, Societe Generale and Goldman Sachs are joint book runners.
Economy Minister Arnaud Montebourg said earlier on Tuesday the state had enough cash available from previous share sales to fund the purchase of the Alstom stake.
Montebourg said that following the sale of shares in Airbus , Safran and Aeroports de Paris, the state now has over 2 billion euros that will be used to buy the Alstom stake.
GDF Suez shares closed 1.3 percent higher on Tuesday, outperforming the CAC 40 index, which ended up 0.1 percent. Based on Monday's close, the shares had risen 20 percent in the year to date and 39 percent over the past 12 months.
(Reporting by Geert De Clercq and Blaise Robinson; Editing by John Irish and William Hardy)