France dominated the match and led 21-15 after 41 minutes, although Norway gradually narrowed the deficit before running out of time while trying to equalize.
Signate Mariama and Baudouin Paul were France's top scorers, with five goals each.
Montenegro defeated Britain 31-19 in the hosts' opening in Group A.
Earlier, three-time Olympic champions Denmark beat Sweden 21-18 in their Group B opening match at the London Games, boosting the Beijing silver medallists ' confidence in their quest for gold this time around.
The teams were neck-and-neck throughout their first ever meeting at the Olympics until Denmark scored four goals in the final minutes.
Denmark will next play South Korea, which defeated Spain 31-27 in the another Group B match on Saturday.
South Korea pulled ahead early to 8-3 and ended the first half with a comfortable 16-12 lead.
Spain, which won bronze in Beijing, struggled to fend off its opponent's fierce attacks led by Eun Hee Ryu, who scored nine goals.
In Group A, Brazil edged Croatia 24-23 after scoring four consecutive goals to gain a comfortable lead 10 minutes before the end of the match.
In another Group A match, Russia defeated Angola 30-27.
The Russians are gold favourites in London. They dominated the game, although the Angolans managed to equalize 23-23 early in the second half. Russia regrouped to wrap up the match with Liudmila Postnova becoming the top scorer with five goals.