Iliad had made its surprise bid in late July in an effort to gain 56.6 percent of T-Mobile, the fourth-ranked cellphone operator in the United States.
The Wall Street Journal reported in August that T-Mobile refused to discuss the takeover possibility with Iliad, or even allow access to its financial information.
In 2011, US regulators blocked AT&T's effort to buy T-Mobile, saying it would be harmful to consumers and competition.
Iliad is owned by a billionaire, Xavier Niel, and is the parent company of Free, a French telecom unit offering phone services, Internet access and television.
T-Mobile's share price fell nearly four percent in early afternoon trading in New York after Iliad's statement, before recovering slightly to $27. Iliad's share price slid 1.8 percent on Thursday to close at 156.15 euros in Paris.
Deutsche Telekom has been looking to sell off T-Mobile for years, but its management is divided on the strategic interest of shedding what is one of the group's main growth centres.