Joyon sailed into Point-a-Pitre just before midnight to take victory in the single-handed race after seven days, 14 hours, 21 minutes and 47 seconds at sea.
The 35-year-old Gabart arrived seven minutes after Joyon, finishing second in the 11th edition of the daunting race dubbed "Formula One on water" due to the six next-generation, high-speed boats taking part.
"It was really an extraordinary race," said Joyon, praising Gabart, whose boat was badly damaged by storms, as "highly brave and committed".
Joyon beat the previous record set by Frenchman Loick Peyron (Banque Populaire VII) in 2014 of seven days and 15 hours. It was his first victory in seven attempts.
All 123 challengers, half of them in small Class 40 boats, left Saint Malo in northwest France on November 4 for Guadeloupe, a French-governed archipelago in the Caribbean.
When Canadian Mike Birch won the inaugural Route du Rhum in Olympus in 1978, he completed the 3,542-mile (5,700 kilometres) course in 23 days and six hours.
Forty years on, Joyon's Idec Sport and Gabart's Macif were two of the vessels called Ultim -- maxi-trimarans which can speed across the waves at 85km/h (45 knots).
The other Ultim skippers included Armel Le Cleac'h, winner of the most recent solo round-the-world Vendee Globe, whose dreams of victory were scuppered when his vessel, Banque Populaire IX, capsized and had to be rescued by a fishing boat.
He was one of four challengers in the fastest Ultim category to drop out after Sebastien Josse, Thomas Coville and Romain Pilliard also hit difficulties, taking refuge in the Spanish port of La Coruna.