Is it a relative clause?

At last summer’s Farnborough Air Show, the chief executive of Boeing, Dennis Muilenburg, was so upbeat about the American planemaker’s prospects he set off alarm bells among aerospace analysts.

Is it a relative clause to modify prospect? Is it wrong to use 'he' here?

No, it's not a relative clause. "... he set off ..." is a that-clause (though the "that" is not explicit) going with the adjective "upbeat". "He was so upbeat that he set off alarm bells." Or rather, filling things out, the that-clause goes with the adjective clause "upbeat about the American planemaker’s prospects" and is part of the comparative construction that begins with "so".

"He" is fine.