The Scandinavians, who have swept aside all before them at the Games, World Championships and European Championship over the last four years, endured a difficult opening as France raced into a 6-1 lead, but they got back into it and closed to 9-10 after 22 minutes of the first half.
But four straight goals opened up France's lead again and they went in at the break 17-12 ahead and they did not let up in the second half, shutting out Norway's late attempts to get back into the game.
The champions pressed right until the end for a way back into it and they could have levelled with the last throw of the ball, but a free throw was bravely blocked.
Earlier, three-time Olympic women's Handball champions Denmark opened their London 2012 campaign with a thrilling 21-18 victory over Scandinavian rivals Sweden.
The Danish women were level with their opponents in the Group B preliminary clash for the majority of the game, but four goals in the final few minutes took them over the winning line, with Sweden unable to match them.
Republic of Korea eclipsed Spain 31-27 while in Group A, Russia outlasted Angola in a game that finished 30-27.
Brazil beat Croatia 24-23 while hosts Great Britain were beaten soundly by Montenegro who prevailed 31-19.