PARIS— Eva Berneke was traveling to meet European officials when Elon Musk posted on his social-media site X that “Ukraine’s entire front line would collapse” if he turned off his satellite internet service Starlink there.

“This is going to be extremely positive,” thought Berneke, a Danish engineer who is the chief executive of Eutelsat , Europe’s smaller rival to Starlink.

Musk’s words sent shudders through Europe’s security establishment. European governments were already nervous about the Trump administration’s tone of disdain for traditional U.S. allies , pressure on Ukraine and pursuit of a rapprochement with Russia . Much of the continent is looking to reduce its reliance on the U.S., including the mercurial Musk .

Owned by Musk’s SpaceX, Starlink is indispensable for Ukrainian soldiers, who have relied on its terminals for communication, drone control and artillery coordination since Russia invaded in 2022.

But Starlink’s dominance has highlighted the risk of relying on a single U.S. company and its unpredictable owner.

European authorities now want Eutelsat, based in a nondescript office district outside Paris, to provide a backup to Starlink in Ukraine as quickly as possible, via its satellite-internet service OneWeb.

In the longer term, they are counting on Eutelsat to help build a space communication network that would make the continent more autonomous.

Doubts abound that Eutelsat can compete with Starlink anytime soon.

“OneWeb is not a suitable alternative to Starlink in any way, shape or form,” said Christopher Baugh, a satellite-industry expert at consulting firm Analysys Mason . “Launching many satellites doesn’t happen overnight.”

Eutelsat wants to increase capacity. The question is how fast—and who will foot the bill. Working in the company’s favor is the momentous geopolitical shift since President Trump returned to the White House.

Berneke, a 56-year-old who professes little taste for politics, said she first noticed the change in mid-February after Vice President JD Vance lambasted Europe’s democracies at a security conference in Munich, alleging that European suppression of free speech and isolation of far-right parties posed a greater threat than Russia.

Soon after, Trump and Vance gave Ukrainian President Volodymyr Zelensky a dressing-down in the Oval Office , and Washington temporarily cut off Ukraine’s military aid and intelligence-sharing—including access to high-resolution satellite images from Maxar Technologies, a vital battlefield resource for Ukraine’s defenders.

Starlink didn’t freeze its services in Ukraine—but Europeans were anxious about the potential vulnerability.

“If SpaceX proves to be an unreliable provider we will be forced to look for other suppliers,” Poland’s foreign minister, Radek Sikorski, wrote on X in early March, responding to Musk’s assertion that Ukraine would collapse without him. Poland pays for around half of the cost of the roughly 50,000 Starlink terminals used by Ukraine’s military and civilian authorities, according to Kyiv.

Musk’s response shocked Europeans: “Be quiet, small man. You pay a tiny fraction of the cost. And there is no substitute for Starlink.”

Berneke said her phone blew up after that. Panicked European officials wanted to know what Eutelsat could deliver in Ukraine, and how fast. “Can you launch more capacity right now?” she said they asked. undefined undefined Berneke pored over her company’s inventory and found 5,000 OneWeb terminals that could go to Ukraine within weeks. Another 5,000 could be sent within a year. Eutelsat is now waiting for a green light from the European Union to deploy the terminals.

“If you can get 5,000 to 10,000 terminals there, it is a real backup option,” said Berneke.

There are currently around 1,000 OneWeb terminals in Ukraine. They are bulkier than Starlink’s slim dishes, and costlier. The starting price of Starlink’s user terminals is less than $400; OneWeb’s start at $3,200.

To truly compete with Starlink, Eutelsat is likely to need billions of dollars in funding from its three biggest shareholders: the French and British governments and a conglomerate controlled by Indian billionaire Sunil Bharti Mittal .

Competition in the satellite-internet sector is heating up. Amazon is preparing a satellite network called Project Kuiper, and China is launching its own.

Eutelsat is “the only non-U.S., non-Chinese constellation that’s going to be out there,” said Berneke. In the new geopolitical context, “that’s become a stronger selling point,” she said.

Worries about Musk’s reliability have even jeopardized Starlink’s bid to win an Italian government contract to provide secure communications. Italy’s right-wing Prime Minister Giorgia Meloni , a friend of Musk’s who has warm relations with the Trump administration, was leaning toward Starlink. But the European backlash against Musk has delayed a decision. Rome says it is examining Starlink alongside alternatives including Eutelsat.

“If you put all your eggs in an American basket, it will not be good for Italy,” said Christophe Grudler, a French member of the European Parliament. “Imagine if tomorrow Musk says: I want to cut the signal to Italy.”

European governments founded Eutelsat in 1977 with the goal of developing and launching satellites independently from the U.S. For decades, the company’s main business was operating satellites 22,000 miles above the Earth’s surface that move in sync with its rotation, with each satellite beaming continuously to a fixed territory. The main customers were television stations around the world.

In 2021, Eutelsat bought a 24% stake in OneWeb, a British company with a network of satellites that traveled much closer to Earth, like Starlink’s.

Low-orbit networks cost more to build because far more satellites are needed for worldwide coverage. Their advantage is that signals need much less time to travel to and from the Earth’s surface, allowing for near real-time communication.

Berneke became CEO in early 2022 after running a Danish IT company. She had no experience in the space industry or of navigating geopolitics. Her crash course began within weeks when Moscow launched its full-scale invasion of Ukraine.

As Russian tanks rolled toward Kyiv, her team learned that tens of thousands of Eutelsat terminals connected to a geostationary satellite serving Europe had shut down. Russian hackers, aiming to disrupt Ukrainian military communications, had exploited a software weakness to upload malware onto the terminals.

“Welcome to space,” Berneke recalled thinking. “Everywhere in Europe, all the terminals died overnight.”

Ukrainian authorities urgently hunted for replacements. A minister asked Musk for help in a post on Twitter, as X was then called. “Starlink service is now active in Ukraine. More terminals en route,” Musk replied.

“Damn,” Berneke thought when she saw the speed of Starlink’s deliveries. undefined

Starlink soon became a lifeline for Ukraine as Russia bombed the country’s telecommunications and other infrastructure. At first, schools, hospitals and bomb shelters used Starlink terminals, but tech-savvy Ukrainian soldiers quickly recognized their potential.

The sleek white terminals, the size of a pizza box, were easy to carry around the battlefield and difficult for the Russians to jam. The number in military use quickly ballooned. Sporadic Starlink outages in fall 2022 that disrupted military operations drove home how dependent the country’s defenders had become.

But Musk’s tweets about the war were tilting toward Moscow’s warnings, including about the risk of nuclear escalation. He tried to set limits on Ukraine’s operations, denying Ukraine’s request to extend Starlink coverage to Crimea to support a naval drone attack on the Russian fleet.

SpaceX, which donated some of the terminals while the U.S. government paid for others, was also complaining about the cost of supporting Ukraine. Poland and other European countries eventually took over most of the funding.

Meanwhile, the EU and France are hoping Eutelsat can get more satellites for its OneWeb service into space quickly. Berneke said the company needs 4 billion euros, or about $4.5 billion, to renew and expand its satellite fleet.

Starlink’s advantages include the large launch capacity of its parent company, SpaceX, whose fleet of partially reusable rockets send hundreds of Starlink satellites into orbit every month. To reach space, Eutelsat often relies on SpaceX’s rockets.

Write to Margherita Stancati at margherita.stancati@wsj.com , Matthew Dalton at Matthew.Dalton@wsj.com and Vera Bergengruen at vera.bergengruen@wsj.com