Backed by billionaire founder Xavier Niel, Iliad made an initial bid worth $15 billion and then raised it but was rebuffed by T-Mobile US's majority owner Deutsche Telekom. Sources familiar with the situation said Deutsche Telekom was unconvinced by the price and by Niel's ability to run the business better than its own managers could.

The aborted U.S. adventure is seen favorably by Iliad investors because many would prefer Niel to focus on organic growth at home and pursue further market consolidation by reviving talks with Bouygues Telecom, the struggling number three mobile network operator in France.

Bouygues' shares closed up 4.6 percent at 25.64 euros on Tuesday while shares in mobile market leader Orange closed up 3 percent at 11 euros on hopes that it would also benefit from a reduction in the number of competitors.

"Now that Iliad has abandoned the U.S. deal, we think it likely that French consolidation hopes will return," wrote Berenberg analysts in a note.

"On our estimates, and in our very conservative M&A scenario, if Iliad pays 8 billion euros to acquire Bouygues Telecom, the deal would remain accretive to its shareholders – without taking into account the possible upside from market repair."

Analysts at banks Kepler, Natixis, RBC and UBC upgraded ratings on Iliad. The volume of Iliad shares changing hands was at 75 percent of the daily average in the past three months.

Previously a fixed line operator, Iliad's arrival in the mobile market in January 2012 sparked a price war that has increased the pressure to consolidate. Mobile prices fell 27 percent last year and 11 percent in 2012, according to the telecoms regulator.

But Iliad is now in danger of becoming a victim of its own success in stirring up the market as rivals offer faster 4G mobile broadband speeds and price erosion is hitting its core broadband business, said Stephane Beyazian, an analyst at Raymond James.

Bouygues has undercut Iliad's broadband prices with a stripped down 19.99 euro per month TV, fixed phone and Internet offer, and has been gaining clients as a result. Iliad's share of broadband customer additions last quarter was about 21 percent, its lowest point since late 2011, according to the analyst.

Iliad is also racing to build out its own mobile network to meet a regulatory requirement to cover 75 percent of the French population by Jan. 12, 2015. It currently pays Orange to carry much of its mobile traffic.

Nevertheless Beyazian said these risks are priced in at Iliad's current share levels.

Harder to quantify is whether investors will begin to apply a discount to Iliad shares to reflect the risk that Niel, who owns 55.35 percent of the company, will look for other large deals in foreign markets.

"I don't think this (failed U.S. bid) has dulled his ambition at all -- maybe frustrated it but not ended it," said an industry banker.

"He thinks he has a business model that he has proven works and can use elsewhere...You can't rule anything out, they are running a slide rule over everything," he said.

In a statement on Monday Iliad said only that it would pursue "its profitable growth policy ... in the interest of its subscribers, employees and shareholders."

(Additional reporting by Alexandre Bokenbaum-Granier; Editing by Andrew Callus and Greg Mahlich)

By Leila Abboud and Gwénaëlle Barzic