The entrepreneur also shared a fake Telegraph article that was posted on X by Ashley Simon, the co-leader of Britain First, the far-Right political party. Mr Musk later deleted his post.
Mr Breton said “any negative effect of illegal content” could lead Brussels to take action against X.
The Frenchman’s letter also referred to the interview between Mr Musk and Trump, which was live-streamed on the platform.
Mr Trump was suspended from X, then known as Twitter, by its former owners, in the wake of the US Capitol riots in January 2021.
The former president’s account was reinstated when Mr Musk took over a year later, but remained mainly inactive until Monday, when it started promoting their interview.
A spokesman for the Trump campaign said: “The European Union should mind their own business instead of trying to meddle in the US presidential election.”
Mr Musk later wrote online that he would be “happy to host” Kamala Harris, the Democratic nominee, on X for a similar interview.
On Tuesday, it emerged that Mr Breton had shared the letter without permission from his boss, Ursula von der Leyen, the European Commission’s president.
A spokeswoman for the cxommission denied that the Frenchman had approval before issuing the missive, suggesting a rift between the two politicians.
“The timing and the wording of the letter were neither coordinated or agreed with the president nor with the college of commissioners,” the spokeswoman told journalists.