France had already gained the finals by posting an insurmountable 3-0 edge with Saturday's doubles victory by Clement and Michael Llodra, and on Sunday completed a 5-0 shutout.
Previous singles winners Llodra and Gael Monfils took the day off, leaving Simon and Clement to play the reverse singles.
Simon posted a 7-6 (7-5), 6-7 (6-8), 6-3 win over Eduardo Schwank and Clement finished up by dispatching Horacio Zeballos, 7-5, 6-1, in just over an hour.
With the victory, France gained the Davis Cup final for the first time since 2002. They will play Serbia, which rallied to defeat the Czech Republic 3-2 in Sunday's other semifinal match-up.
Argentina fell to 0-5 in Davis Cup matches against France.