Laetitia Nadji, who is in her 30s and has 60,000 followers on her YouTube channel where she gives environmental tips, was chosen for a European version of a similar interview YouTube did with US President Barack Obama.
She chose to ask about the tax policies of Juncker's native Luxembourg and how the EU member state dealt with the profits of multi-national companies.
In an unedited version of the interview posted on YouTube, she asked Juncker if, as a former finance minister and premier of Luxembourg, he was best-placed to "put an end to this injustice".
With a pixellated face, the man is heard telling her: "It's an extremely difficult question for Mister Juncker to answer because you're getting into companies and lobbying. Also, you don't want to offend the European Commission and YouTube and all the people who believe in you. At least, if you want to have a long career on YouTube."
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Nadji said in a later post on YouTube: "At one point, I felt threatened."
Nadji said she was surprised that following the interview, she was summoned to Google's offices, only to be offered a one-year contract as one of its brand "ambassadors".
Although it was her "dream", she said she turned it down because she did not want to be "manipulated".
YouTube denied putting pressure on Nadji, saying only it had asked her to be "respectful" to Juncker.
A spokesman said YouTube regretted that an "unfortunate sentence" from its employee was being interpreted as a warning.
It said Juncker "has spent 25 years in public life taking questions from some of the most seasoned journalists of our time. He neither needs nor would he allow anyone to attempt to soften up questions for him."
The Commission added in its statement that Juncker was "very pleased" with the interview.
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