Hosts France had to settle for silver while Denmark earlier took the bronze medal with a 30-25 win over Sweden.
The final was fast-paced from the start, with nearly a goal per minute as the Nordics ended the first half up 15-13, with Norwegian centre backs Stine Bredal Oftedal and Henny Reistad contributing four points each.
That lead grew to 27-20 in the second half but defending champions France surged in energy, with French left back Orlane Kanor and centre Tamara Kovacek combining for nine points overall.
The Tokyo gold medallists ultimately failed to convert enough attempted shots into goals as the clock ran down, however, with Norwegian goalkeeper Katrine Lunde making 12 saves by the time the final whistle blew.
French fans nonetheless united to belt out Edith Piaf's iconic song "Je ne regrette rien" to support their defeated team.