The deal would involve Iliad acquiring 56.6 percent of T-Mobile for $15 billion in cash, or $33 a share, and the remaining 43.4 percent of the U.S. company would be worth $40.50, on account of cost saving measures, putting the entire deal at 17 percent higher than T-Mobile's closing price Wednesday.
T-Mobile has not yet responded to the offer.
Iliad, like T-Mobile, has taken the French telecommunications segment by storm by offering cutthroat prices and said the offer would be a "one-time opportunity to enter the world's-largest telecoms market," according to a person familiar with the deal.
"The U.S. mobile market is large and attractive," Iliad said in a statement. "T-Mobile US has successfully established a disruptive position, which in many ways, is similar to the one Iliad has built in France."
T-Mobile and Sprint have been working for months to close a $30 billion merger, which is being investigated for antitrust issues. Iliad said its acquisition of T-Mobile would not lead to any such issues as it does not have a presence in the U.S. market.
As of 3 p.m., T-Mobile was up 6 percent and competitors Verizon and AT&T were down 2.3 percent and 1.7 percent, respectively.