Eutelsat said it was "currently evaluating a possible offer for Inmarsat", although there was no certainty an offer would be made.
The move comes after Inmarsat said earlier this month it had rejected a takeover approach from EchoStar, a U.S. company which has continued to build a stake in Inmarsat.
Inmarsat's shares were up more than 4 percent in late trading to 632 pence, giving the group a market capitalisation of 2.9 billion pounds.
Analysts had already identified Eutelsat, along with ViaSat, as a possible counterbidder to EchoStar.
Colorado-based EchoStar, which has until July 6 to make a firm offer or walk away from the FTSE 250 group, had built a near 3 percent shareholding in Inmarsat, as well as a 10.4 percent position in its convertible bonds, as of Friday.
Analysts at Jefferies, who have a "buy" recommendation on Inmarsat, said they viewed an offer from Eutelsat to have only limited industrial logic, and said Inmarsat's spectrum holding in the United States would have more appeal to EchoStar.
"Collectively our base case therefore remains that, should a recommended offer emerge, it will be from EchoStar", they said.
(Reporting by Paul Sandle; editing by Kate Holton and Jan Harvey)