Maxime Medard came closest to registering the game's only try but Contemponi came to the rescue for Argentina, pulling the French full back down just short of the line.
The result was in doubt until the very end of the encounter, with the Skrela kicking the hosts six points clear with two minutes remaining.
The match was the first between the two sides since last year's third and fourth place play off at the World Cup, with the Pumas having won that clash and the tournament's opening fixture against the same opponents.
France now take on the Pacific Islanders and then Australia, while Argentina face Italy and Ireland.
