France's Iliad challenges Sprint for control of T-Mobile

* Iliad bids $15 billion cash for 56.6 pct at $33 per share

* Deal to be financed with cash and equity; banks lined up

* Sets up potential bidding war with Sprint

* Iliad faces fewer antitrust issues than Sprint (Adds no comment from Softbank in paragraph 6)

By Leila Abboud and Soyoung Kim

PARIS/NEW YORK, July 31 (Reuters) - French telecommunications company Iliad SA has made a surprise offer for T-Mobile US Inc, setting up a potential bidding war with Sprint Corp, the U.S. mobile carrier now controlled by Japan's Softbank Corp.

The approach will further shake up a U.S. media and telecoms market already in tumult as a series of U.S. cable and cellular operators have bid for rivals to cut costs amid slowing growth. The market and its relatively healthy margins remain alluring to some foreign operators like Softbank and Iliad, however.

Iliad, which has shaken up the French mobile and broadband market in the past decade with its cheap, pared-down subscriber plans, bid $15 billion in cash for 56.6 percent of T-Mobile US at $33 per share, it said in a statement on Thursday.

The Paris-based company said its offer for the fourth-largest U.S. carrier values all of T-Mobile at $36.20 per share, a premium of 42 percent to the pre-announcement share price, once expected cost savings of $10 billion were taken into account.

That is less than the roughly $40 per share Sprint agreed to pay under the broad terms of an agreement worked out with Deutsche Telekom AG, T-Mobile's majority owner. The terms of that proposal, which followed months of talks and which was reported by Reuters in early June, would value T-Mobile at nearly $32 billion.

Deutsche Telekom and Sprint declined to comment. A spokesman for Softbank in Tokyo also declined to comment.

Despite Iliad's lower offer, three people close to the French company said founder Xavier Niel believes he has a strong card to play because his bid would not face the antitrust scrutiny that confronts Sprint in trying to merge the third and fourth-biggest U.S. mobile operators.

"SoftBank has been told in many very clear coded words that the Department of Justice and the FCC would probably not approve the acquisition," said Reed Hundt, a former chairman of the U.S. Federal Communications Commission. "There's no question to me that the FCC would say 'bienvenue'" to the proposed Iliad deal.

The FCC and Department of Justice expressed a desire earlier this year to have at least two more network operators competing against AT&T and Verizon.

The T-Mobile offer is Niel's most audacious attempt at extending his reach beyond France, Monaco and Israel, where he owns part of operator Golan Telecom. Still, his bid to enter the United States mobile market is a long shot, some investors and analysts say.