The 29-year-old added a second goal with a superbly angled shot before Norway, who had qualified in second place and rested 10 of their 11 first-choice starters, including top scorer Erling Haaland, pulled one back when the unmarked Thelo Aasgaard scored a minute later.
Dembele bagged his first World Cup treble with a fine finish in the 32nd before Norway's Jorgen Strand Larsen had a penalty saved five minutes after the restart.
France, who got a fourth goal through Desire Doue in stoppage time, will not know their Round of 32 opponents until Saturday when all group matches are completed but are likely to face Sweden, while Norway will take on Ivory Coast in the knockout stage in Dallas on 30 June.