The three-times British champion jockey, 41, tested positive for what is believed to be cocaine following a routine examination at Longchamp on September 16.
Dettori's suspension runs from November 20 to May 19 and is likely to be reciprocated by racing jurisdictions worldwide, including the British Horseracing Authority.
Stewart-Moore said in a statement that Dettori "fully accepts" France Galop's decision to ban him for six months.
"France Galop have today announced their finding Frankie Dettori has committed a breach of their rules relating to prohibited substances," said Stewart-Moore.
"I have spoken to Frankie since the announcement was made and he has told me he fully accepts France Galop's decision.
"He also accepts that he has let down the sport he loves and all those associated with it, as well as the wider public.
"But most of all, and this is his greatest regret, he has let down his wife and children."
With the BHA set to reciprocate France Galop's suspension, he will back in time to feature in the Derby and the Oaks at Epsom - and at Royal Ascot in June.
Italian-born Dettori, who will be 42 on December 15, had four rides at the Prix de l'Arc de Triomphe trials meeting on September 16, after which the sample was returned.
The case was then put before the medical commission of France Galop in Paris on November 20.
It was announced a day later that he was temporarily suspended from competing in France on medical grounds.
Dettori's hearing concluded at France Galop's headquarters in Paris on Tuesday.
Stewart-Moore said his client had received "a sympathetic hearing".
Dettori, who was cautioned by police for possession of cocaine in 1993, has vowed to "rebuild his reputation" once he has served his suspension.
Stewart-Moore said: "He is enormously grateful for the opportunities that he has been given by owners and trainers over the years, and for the support of his many fans.
"Racing has been good to Frankie and he knows that his privileged position brings with it responsibility.
"For this reason he is determined to rebuild his reputation when he returns to the saddle.
"Frankie could make excuses. He has, after all, regularly been tested for prohibited substances throughout his career.
"He is clear, however, that the responsibility for his current situation lies squarely with him.
"From the start of France Galop's inquiry he has acknowledged to them he has made a mistake and that the fault was his.
"Finally, he has asked me to thank everyone for the many messages of support he and his family have received."
Dettori made the headlines in October when his 18-year association with powerful owners Godolphin came to an end, with the rider planning to operate as a freelance in 2013.
He partnered nine English Classic winners in the royal blue silks, including their first in 1994 Oaks victor Balanchine, and a total of 110 Group or Grade One winners for the owner.
A host of Dettori's big-race winners have been trained by Godolphin handler Saeed bin Suroor, including four of those that formed the rider's 'Magnificent Seven' at Ascot on September 28, 1996.
Dettori is not the first to fall foul of the French authority, with Kieren Fallon banned for six months by France Galop in 2006 after returning a positive test for a metabolite of a banned substance.
France Galop then suspended him a further 18 months after a second positive test in August 2007.