Reality TV
Giraud had sung Bryan Adams's 'Have You Ever Really Loved A Woman' as the top seven performed songs from movie soundtracks.
He was joined in the bottom three by Anoop Desai and Lil Rounds, with Desai there for the third week in a row.
After the results of the public vote were revealed, judge Simon Cowell said: "We've come to a decision. Matt, it's good news."
As the other finalists joined Giraud in a group embrace, Cowell added: "I wouldn't be so quick to congratulate him."
When the top seven return next week to sing disco numbers, there will be no possibility of the judges saving a contestant, and two finalists will be eliminated from the show.
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