The John Gosden-trained filly is only the eighth horse to achieve the double with Dettori winning it for a sixth time.
But the odds-on favorite was given an almighty scare by another filly, Sea of Class under James Doyle, who came with a dramatic late run and was a stride away from causing an upset.
Cloth of Stars finished a creditable third.
Irish and Yorkshire Oaks winner Sea of Class was last entering the straight but weaved through the field to almost catch Enable, who was well-placed throughout and timed her run to perfection under the wily Dettori.
Sea of Class trainer William Haggas was proud of her efforts: "She got beaten by a champion, Enable is a great horse."
Enable was a lauded winner of last year's Arc, but missed most of this year's campaign through injury before an impressive return at Kempton left her as the pre-race pick by most experts.
"She wasn't at her best today," admitted Gosden. "It's entirely down the filly and her guts and she was given a lovely ride by Frankie."
Gosden, who has won the Arc three times, also hinted Enable may stay in training as a five-year-old in an attempt to win the monument for an historic third time.
Dettori said it had not been easy: "I was riding in the Arc for the 30th time and I was more nervous than ever.
"I waited as long as I could and at the 300 pole she showed her trademark turn of foot."
The Arc, run over a mile and a half (2,400m), was back at the famous racecourse in Paris after the last two runnings at Chantilly while it was being redeveloped.
It is the third richest on the calendar after the Pegasus World Cup and the Dubai World Cup, but over the years has attracted the cream of the crop from thoroughbred racing.