The eight-month, 39,270-nautical mile (72,728km) race was decided when Cammas's Groupama 4 boat finished second in the ninth and final leg, a short 550-mile sprint from Lorient in France.
The result gave Cammas an unassailable 24-point lead with the Galway in-port race to complete on Saturday.
"This is an incredible moment for me," said Cammas, who follows 1985-86 winner Lionel Pean as the only French winner of the 39-year-old offshore event, formerly known as the Whitbread Round the World Race.
"It was always my dream just to participate in this race. The first book I ever read was about this race and it hasn't sunk in yet."
It was the first time that France had competed in the race for 18 years and Cammas was considered a big outsider despite a big reputation in his home country as a single-handed and team sailor.
At one stage, Cammas and his team were 28 points behind Telefonica, winners of the first three legs, but a remarkable resurgence over the second half of the race, coupled with a drop in form for the long-term leaders, turned the tables completely.
"The race started badly for us but every single member of the team raised their level and that's what saw us home," Cammas said.
Standings after the final offshore leg
1. Groupama (France) 250 points
2. Camper/ETNZ (Spain/New Zealand) 226
3. Pima (U.S.) 220
4. Telefonica (Spain) 209
5. Abu Dhabi (UAE) 124 + 5 or 10
6. Sanya (China) 40 + 5 or 10