Davies, 29, opted for intermediate tyres and it paid off as Rea and Tom Sykes were among those forced to change tyres on a drying track.
Dutchman Michael van der Mark was just under 10 seconds behind Davies with Sykes completing the podium positions.
Englishman Sykes' third place trimmed Rea's championship lead to 44 points.
Davies, who was in 13th spot early in the race, remains in third spot in the championship but is still 86 points adrift of defending champion Rea.
After gaining his first pole position of this year's championship in qualifying, Northern Irishman Rea, 29, led early on but was passed by his Kawasaki team-mate Sykes before the end of the first lap.
With the tyres choice having a huge impact on the race, Leon Camier moved into the lead by lap seven and it was at that point that both Rea and Sykes, 31, opted to make their tyre changes.
Lorenzo Savadori led for a time before Davies moved to the head of affairs and the Welshman pushed on to win by 9.8 seconds.
Rea, after dropping to ninth spot following his tyre change, produced a late charge to move up to fourth with Savadori fifth, Frenchman Mattieu Lagrive next and Camier eventually ending up seventh as his intermediate tyres began to lose grip.
The riders will be back in action on Sunday for the second race at Magny-Cours and, after this weekend, the two remaining rounds of the championship will be in Spain and Qatar.
Welshman Chaz Davies earned his sixth win of this year's World Superbike Championship as series leader Jonathan Rea took fourth at Magny-Cours.