(Fixes detail on Alstom bailout and Sarkozy in line 45)
* After losing out on SFR, Bouygues finds Alstom solution
* Alstom exit cash could help bolster Bouygues Tel
* UBS estimates Bouygues getting 2 bln euros
* Bouygues Tel to detail fixed broadband strategy Thursday
* Shares close down 2 pct
By Leila Abboud and Gilles Guillaume
PARIS, June 23 (Reuters) - Bouygyes will gain more financial muscle to support its flagging telecoms business as a result of a deal agreed at the weekend to sell most of its holding in engineering group Alstom to the French state.
Martin Bouygues, the 62 year-old tycoon who runs the politically influential construction-to-television group founded by his father, has chalked up a win on the Alstom takeover saga only two months after losing a battle to buy larger mobile operator rival Vivendi's SFR.
Bouygues had long seen its 29 percent stake in Alstom, worth some 1.7 billion euros ($2.31 billion) at current market prices, as peripheral to its strategy. It supported the sale of Alstom's energy business to General Electric since the U.S. company made its bid in April.
But Bouygues' position was complicated after the French government initially began pushing a rival bid from Germany's Siemens and Mitsubishi Heavy Industries.
On Sunday, Alstom's board backed the proposed tie-up with GE and France secured an option to buy 20 percent of Alstom from Bouygues after overcoming a disagreement over price.
Although some French media outlets portrayed the government as having forced Bouygues' hand, sources close to Bouygues said on Monday that the company was comfortable with the outcome because it got reasonable value for its Alstom stake while ensuring a promising future for Alstom.
"Bouygues gets access to a pile of cash and finds a solution for Alstom," one person close to the company said.
"It will also put an end to people saying that Bouygues needs to sell its telecom business quickly since the proceeds from the Alstom sale will help pay down debt and alleviate any financing issues."
UBS analysts estimated that Bouygues' sale of the Alstom stake could bring in as much as 2 billion euros and cut its net debt to EBITDA (core earnings) ratio to less than 0.5 times compared with 1.3 times currently.
Under the deal, the French government secured an option to buy up to 20 percent of Alstom from Bouygues - which includes a 2-5 percent discount - at any point when the market price is 35 euros or more in the next 20 months.
In exchange, Bouygues will lend Alstom stock commanding 20 percent of voting rights to the state and surrender two board seats, allowing the state to exercise an immediate role.
Bouygues bought most of its Alstom stake in 2006 at more than 60 euros a share following a bailout of the train and turbine maker by then finance minister Nicolas Sarkozy.
Bouygues had to write down its value by 1.4 billion euros in February, and did not want another massive charge to weigh on its balance sheet if the government bought the Alstom shares at current market prices of around 28 euros.
Bouygues shares closed down 2 percent at 31.64 euros.
Telecoms has been Bouygues' most pressing problem since low-cost player Iliad arrived on France's mobile scene in January 2012, touching off a price war that is increasing the pressure to consolidate.
Bouygues, hardest hit because of its smaller size, plans to cut 17 percent of its staff to reduce costs to ensure its survival in a market where mobile prices fell by nearly one-third last year.
After missing out on SFR, Bouygues held informal talks with mobile market leader Orange over a sale, as well as with Iliad, sources close to the situation have said.
Those talks have so far come to nothing because of differences over price, but those involved did not rule out that a deal could be reached later.
A London-based telecoms analyst, who declined to be named, said that the cash from the Alstom deal could strengthen Bouygues' hand when negotiating with Orange and Iliad.
Another tactic for Bouygues is to take the mobile price battle to the fixed broadband market with a TV, Internet and fixed-line phone bundle at 19.99 euros a month. This is targeted at Iliad, which has similar offers from 29.99 euros a month, but will also hurt Orange, which has a big fixed customer base, according to analysts.
Bouygues will hold a press conference on Thursday to give more details of its new push in fixed services.
"Bouygues will also certainly have more cash to sustain the telecom business, but there is a risk that it just burns through it by cutting prices in the fixed market," the London-based analyst said.
The first person close to Bouygues put it in starker terms. "If the consolidation deadlock persists, we will all get in a sinking ship and sing as it goes down," the person said.
"The Alstom money just means that Martin Bouygues' boat has a lot of lifeboats and can stay afloat and protect his people a bit longer."
A spokesman for Bouygues declined to comment. ($1 = 0.7357 Euros) (Additional reporting by Gwenaelle Barzic; Editing by Jane Merriman)