Scrum-half Morgan Parra opened the scoring with a penalty in the 11th minute after Pumas counterpart Nicolas Vergallo threw a punch in a ruck - but an offside from Parra helped fly-half Felipe Contepomi square things up six minutes later.
Parra converted another penalty in the 26th minute and increased the lead to 9-3 five minutes later after Argentina had been penalised for an infringement at a ruck.
Contepomi's 46th-minute penalty reduced the arrears but fly-half Damien Traille made it 12-6 with a 49th-minute drop goal.
Parra booted his fourth penalty just before the hour mark after Argentina collapsed a scrum, but Contepomi did likewise two minutes later after debutant winger Yoann Huget failed to release the ball.
Argentina move on to play Ireland this weekend.
France: Palisson; Huget, Rougerie (Porical 79), Jauzion, Andreu; Traille (Estebanez 78), Parra (Yachvili 78); Mas, Servat (Guirado 65), Domingo (Thion 56), Nallet, Pierre (Ducalcon 56), Chabal (Harinordoquy 62), Bonnaire, Dusautoir (capt).
Argentina: Rodriguez; Camacho, Tiesi, Fernandez (Bosch 66), Amorosino; Contepomi (capt), Vergallo; Scelzo (Ayerza 49), Ledesma (Creevy 64), Roncero, Albacete, Galarza, Fernandez Lobbe, Achaval (Cabello 41), Fessia (Galindo 66).