Ogier, driving a Volkswagen Polo, won the event in the Alsace region by 12.2 seconds from Spain's Dani Sordo (Citroen) while Finn Jari-Matti Latvala took third place 7.3 seconds further behind.
On the first stage of the final day, Loeb's Citroen slid off the road and ended up on its roof in a ditch, according to the world rally championships' website (www.wrc.com).
Loeb, who won a record nine world titles from 2004-12, and co-driver Daniel Elena escaped unhurt.
"I lost the rear in a fast right corner, and then we had a spin and I finished in the ditch. And that was the race over. I would have preferred to have finished my last rally here, but it didn't go according to plan," said the Frenchman.
Loeb competed in only four rallies this season after deciding not to defend his world title. He won the Monte Carlo Rally and Rally Argentina and finished second in Rally Sweden.
Ogier succeeded Loeb as world champion on Thursday after his only rival, Belgian Thierry Neuville, failed to claim the power stage at the Rally of France.
"There has been so much emotion this weekend," Ogier said after his seventh win of the season.
"After the excitement of winning the title on Thursday, it was difficult to get back into the race. But we couldn't stay like that all weekend and decided to react yesterday.
"We pushed to the maximum then and this morning we soon made a gap at the front. Then we had to bring the car home, which wasn't easy in the rain and mud. We started the story from zero with Volkswagen last year, and now we're close to the manufacturers' title as well."
The penultimate rally of the season will be held in Spain from Oct 24-27.
(Reporting by Julien Pretot; Editing by Amlan Chakraborty, Josh Reich and Alison Wildey)
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