British time-trial expert David Millar won the third and final leg of the weekend race, a 7.7-kilometer (4.8-mile) race against the clock in and around the town of Porto Vecchio.
Millar clocked 9 minutes, 49 seconds, outpacing second-place Contador by two seconds. Australia's Michael Rogers was third, with a time of 9:53.
"It felt really good. I really enjoyed it," said Millar.
It was a good day for British cyclists: Russell Downing led a mass sprint to win the second stage Sunday morning - a mostly flat 75-kilometer (47-mile) course in and around the Corsican port town.
Armstrong, who insists he is still far from top form in the run-up to the Tour in July, clocked 10:08 and finished 15th in the time trial. But he said his form in the discipline is improving.
"It was hard to find a rhythm, but I felt better than I did in Murcia," Armstrong said of the time trial in his last race - the Vuelta de Murcia in Spain earlier this month. "I felt steadier." "It was a good as it could be for two days. Yesterday was an extremely hard day," he added.
After Saturday's stage, a wind-swept 175.5-kilometer (109-mile) ride with an uphill finish, Armstrong said he had a "really, really bad" day - and struggled on the last climb.
In the final standings, Fedrigo - who won Saturday's stage - outpaced Rogers in second by 14 seconds. Young Portuguese cyclist Tiago Machado of Team RadioShack was third, 15 seconds back.
"I'm 31 years old but I still don't know my limits, I still surprise myself," Fedrigo said. "It's not like winning the Tour - the Tour is another dimension - but the Criterium International was the biggest race this year so far in terms of the participants, and I'm proud to have won it."
Contador finished 15th overall, 1:08 behind the Frenchman, while Armstrong was 47th, 5:05 back.
The race was the first on the Mediterranean island of Corsica since 1982, and local officials are hoping to host a Tour de France stage in coming years.
