I believe the version they played was sung by Frank Sinatra. However, this song became famous when Fred Astaire sang in his 1936 hit American musical comedy film Swing Time. The character played by Fred sings to Ginger Rogers who in the scene doesn’t feel at all beautiful as she was busy washing her hair and getting ready. This song went on to win the Academy Award for Best Original Song that year. But it was originally recorded as a duet by Bing Crosby and his then wife Dixie Lee earlier the same year. The lyrics were slightly different from Fred Astaire's version. In later years this song has been re-sung by several other singers, to name a few like Tony Bennett, Doris Day, Ella Fitzgerald, Frank Sinatra, Rod Stewart, Maroon 5 and many more.
Here's Frank Sinatra's version which I am sure was the one played as background for Roger Federer.
Lyrics in English:
Some Day, When I'm Awfully Low
Yes, You're Lovely
With Each Word Your Tenderness Grows
Lovely, Never, Never Change
And That Laugh Wrinkles Your Nose