Jack Brabham won the French Grand Prix 1960 at Reims-Gueux on 3 July 1960, starting from pole position. Olivier Gendebien finished second for Cooper-Climax, with Bruce McLaren completing the podium for Cooper-Climax.
| Pos | Grid | Driver | Team | Laps | Time / Status | Pts | FL |
|---|---|---|---|---|---|---|---|
| 1 | 1 | Jack BrabhamBRA | Cooper-Climax | 50 | 1:57:24.9 | 8 | |
| 2 | 9 | Olivier GendebienGEN | Cooper-Climax | 50 | +48.3 | 6 | |
| 3 | 7 | Bruce McLarenMCL | Cooper-Climax | 50 | +51.9 | 4 | |
| 4 | 12 | Henry TaylorTAY | Cooper-Climax | 49 | +1 Lap | 3 | |
| 5 | 10 | Jim ClarkCLA | Team Lotus | 49 | +1 Lap | 2 | |
| 6 | 14 | Ron FlockhartFLO | Team Lotus | 49 | +1 Lap | 1 | |
| 7 | 4 | Innes IrelandIRE | Team Lotus | 43 | +7 Laps | 0 | |
| 8 | 15 | Bruce HalfordHAL | Cooper-Climax | 40 | Engine | 0 | |
| 9 | 17 | Masten GregoryGRE | Cooper-Maserati | 37 | +13 Laps | 0 | |
| 10 | 22 | Ian BurgessBUR | Cooper-Maserati | 36 | +14 Laps | 0 | |
| 11 | 5 | Wolfgang von TripsVON | Ferrari | 30 | Transmission | 0 | |
| 12 | 2 | Phil HillHIL | Ferrari | 29 | Transmission | 0 | |
| R | 8 | Jo BonnierBON | BRM | 22 | Engine | 0 | |
| R | 15 | Lucien BianchiBIA | Cooper-Climax | 18 | Transmission | 0 | |
| R | 6 | Dan GurneyGUR | BRM | 17 | Engine | 0 | |
| R | 19 | Gino MunaronMUN | Cooper-Castellotti | 16 | Transmission | 0 | |
| R | 11 | Willy MairesseMAI | Ferrari | 14 | Transmission | 0 | |
| R | 13 | Tony BrooksBRO | Vanwall | 7 | Vibrations | 0 | |
| R | 3 | Graham HillHIL | BRM | 0 | Accident | 0 | |
| R | 18 | Maurice TrintignantTRI | Cooper-Maserati | 0 | Accident | 0 | |
| W | 20 | Richie GintherGIN | Scarab | 0 | Engine | 0 | |
| W | 21 | David PiperPIP | Team Lotus | 0 | Engine | 0 | |
| W | 23 | Chuck DaighDAI | Scarab | 0 | Engine | 0 |