Japan enjoyed the best of the early possession, but the first real chance of the afternoon fell to the French.
Japan made 2-0 moments into the second period when Mizuho Sakaguchi stooped low to head past Bouhaddi from close range.
Marie-Laure Delie might have cut the deficit to 2-1 after 55 minutes, but Fukumoto palmed the ball to safety.
France continued to probe as the second half developed, with Delie and Necib remaining their biggest threats. Their best chance of the second period fell to Necib after 71 minutes, but Fukumoto got down low to thwart the danger.
France did find the net five minutes later, however, when Eugenie le Sommer struck from close range with a powerful effort.
They had a glorious chance to level five minutes later, but Elise Bussaglia missed from the penalty spot after Le Sommer had been felled in the box.
France continued to press in the latter stages, but they could not level as Japan advanced to the final, where they will meet either Canada or the United States.