"We have a lot of customers who want us to get there quickly," Eva Berneke told AFP in an interview.
"They tell us they took Starlink because there wasn't anyone else. But they want competition too. Nobody wants a monopoly."
Eutelsat recently merged with British operator OneWeb and is aiming to add telecoms and connectivity to its main business of broadcast media.
But Musk is not the only competitor.
US magnate Jeff Bezos and the Chinese government also have ambitions to launch thousands of satellites.
"There's room for four or five operators," Berneke said of the emerging industry, comparing it to mobile phone networks.
Satellite broadband promises to bring coverage to the most remote areas by doing away with the need for antennas and other infrastructure.
It will also supply internet to passenger planes and products like connected cars.
- 'Anything is possible' -
Eutelsat plans to release a second generation of OneWeb internet services by 2028.
Berneke is also planning to get on board with a six-billion-euro EU project called IRIS2, which will aim to launch a network of satellites.
Eutelsat is part of a consortium negotiating with the EU and Berneke said she could envisage OneWeb payloads on IRIS2 satellites and vice-versa.
"At this stage, anything is possible," she said.
However, there are some thorny issues to be thrashed out.
OneWeb is a subsidiary of Eutelsat, but the British government has a "golden share" in the company -- the kind of control that worries some in the IRIS2 setup.
Berneke said she had set up a "security committee" to ensure that only authorised people could access sensitive aspects of the project.
The consortium is aiming to close a deal by early next year, but she acknowledged there are plenty of issues to be sorted out, not least the involvement of non-EU elements in OneWeb.
But Berneke highlighted that European launch facilities were thin on the ground right now.
"If we insist on launching something that needs to be operational in 2028 and for the launcher to be European, we will have a hard time, it's as simple as that," she said.
Satellite-based Internet technologies
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