The man who fell to Earth is correct. Earth is a proper noun, therefore it should be capitalized.

’The Man who fell to Earth' is the title of both a novel, by Walter Tevis, and the film based on it, as Claire has said, starring David Bowie. In any other context, you would say ’the man who fell to the ground’.

The film is called 'The man who fell to Earth'. There is also a series, which looks like a remake.

They are both correct.

They both sound right to me. I do not see an issue with how either one of those are written 🤔