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The negotiations accompany a softened line on sector consolidation from the government, which holds 25 percent of Orange, after it opposed a 10 billion euro (7.37 billion pound) bid last year for Bouygues Telecom by tycoon Patrick Drahi's Numericable-SFR.
Competition concerns could allow Numericable-SFR and France's fourth mobile operator, Iliad, to scoop up assets if disposals are required.
A deal would mean a return to three mobile operators in France four years after the arrival of Iliad's Free Mobile low-cost services led to a protracted price war.
Former state monopoly Orange held three-way talks with Iliad and Bouygues about a consolidation deal in 2014, encouraged by the government, but they collapsed over valuation and how to divide Bouygues Telecom between the two buyers.
Orange said on Tuesday that there was no time limit on talks "with a view to a consolidation with Bouygues Telecom," nor was there any commitment to any particular outcome. It added that it was exploring opportunities in the French telecoms market.
Bouygues said in a separate statement it had signed a confidentiality agreement with Orange.
"As it is interested in opportunities that would enable it to bolster its long-term presence in the telecoms sector, Bouygues announces that preliminary discussions have started with Orange to look at the possible options," Bouygues said.
STUMBLING BLOCKS
The main issues in the negotiations would be jobs, investment in infrastructure and especially fibre optic networks, and antitrust-related disposals, a source familiar with the matter said.
"The idea is that Bouygues becomes a significant shareholder in Orange's capital with a stake quite close to that of the state, and the bulk of the transaction will be in shares," the source said.
Weekly newspaper Le Journal du Dimanche said at the weekend that Orange was looking at buying Bouygues Telecom for 10 billion euros in cash and shares, with Bouygues to receive a 15 percent stake in Orange valued at 8 billion, and the rest in cash.
A previous attempt by Drahi -- whose Altice holding company controls Numericable-SFR -- to buy Bouygues Telecom met with opposition from French Economy Minister Emmanuel Macron, who said it could destroy jobs and risked creating a French operator that was "too big to fail".
Last month, however, Macron said he was not opposed in principle to further deals in the sector. Consolidation talk had been rekindled after an auction of 4G spectrum helped to clarify the balance of power in the sector.
Bouygues Telecom, France's third-largest mobile operator, has also said it could prosper on its own, after responding to the price war with a turnaround plan including staff cuts and a focus on rolling out its 4G network and the fixed-line broadband market.
Orange Chief Executive Stephane Richard has said consolidation in France was lagging other major European countries, and that ultimately the group would have a role in Europe-wide mergers once there were signs the region was heading towards a single telecoms market.
Two sources with direct knowledge of the matter told Reuters last month that Orange had hired investment banks Morgan Stanley and BNP Paribas to assess the merits of doing a deal with other network operators in Europe.
Shares in Orange were up 0.6 percent by 1140 GMT, while Bouygues' were 1 percent higher. Shares in Numericable-SFR leapt 10 percent, while Altice was trading up 5.6 percent. Iliad shares were 2.6 percent firmer.
Orange's advisers include Messier Maris and Associates, while Bouygues is being advised by Rothschild, HSBC and Darrois.
(Additional reporting by Emiliano Mellino in London; Writing by James Regan; Editing by Andrew Callus and Keith Weir)
By Gwénaëlle Barzic and Matthieu Protard
