Successful with Le Havre in 2009, Rouget sent out the son of Wootton Bassett to take the Classic by a length and a half.
Rouget also saddled leading fancy Mekhtaal, but he could never get near enough to challenge after being last turning for home.
Jean-Bernard Eyquem, winning the race for the first time, brought Almanzor through with a well-timed challenge after Harry Dunlop’s Robin Of Navan had made most of the running.
The Aidan O’Brien-trained Bravery flattered briefly, while Andre Fabre’s Talismanic, wearing the Godolphin colours, had every chance.
Zarak came with a late rattle to claim second spot, with Dicton also putting in good late work to take third place, another length and three-quarters away.
The John Gosden-trained Foundation, sent off the 4-1 favourite, was a big disappointment and finished well beaten.
The Roger Charlton-trained Imperial Aviator, who was supplemented by connections, also failed to live up to expectations.
Almanzor was given quotes of around 16-1 for the Prix de l’Arc de Triomphe.
Rouget said: “He is improving, and I had no doubts at all about the trip or his condition coming into the race.”
Rouget added: “We always thought he had a chance - we wouldn’t have run him otherwise.
“We have no plans at the moment, but he’ll be a better horse on better ground.”
Charlton said of Imperial Aviator, who only beat Foundation home in the 16-runner race: “The ground was too soft and he lurched about a furlong and a half out.”