Defender Laura Georges opened the scoring with a powerful header just before halftime, and the French then poured in the goals near the end.
Substitute Elodie Thomis scored one goal and set up another two for Marie-Laure Delie and Camille Catala, with Wendie Renard netting inbetween.
The win puts France in second place in Group G ahead of North Korea on goal difference with three points.
North Korea's defence lost its concentration during a corner just before halftime, allowing Georges to run unmarked in from the left to head in the opener past goalkeeper Jo Yun Mi. Until then, North Korea's defence was well organized, stifling France in the first half.
But North Korea lacked imagination going forward for the most part, punting hopeful long balls upfield.
Thomis then provided a spark for France when she came on as a substitute. She added the second goal in the 70th minute, then set up Delie for the third a minute later. Thomis made a quick run down the right before squaring to her fellow forward, who fired the ball in from close range.
Renard netted a header from a corner in the 81st, and Catala completed the rout with another header in the 87th after Thomis fired in a cross from the right.
"We have the three points and we're second in the group," France coach Bruno Bini said. "Now, we're just focusing on getting to the quarterfinals. At the beginning of the match, the players were nervous. In the second half, we played high quality football."
North Korea faces the group leader United States in the last group match, and France will take on Colombia.
Coach Sin Ui Gun believed that the late kickoff in North Korea's previous match because of a flag dispute may have affected his team's preparations. London Olympic organizers displayed a South Korean flag alongside a North Korean player on stadium screens at Hampden Park for the match against Colombia.
"Because of the delay, we had to finish the game late," Sin said. "So maybe it affected our players' ability today."
"We still have one more match to go," he said. "Today's match is a good lesson and will motivate our team."