Jim Clark won the French Grand Prix 1963 at Reims-Gueux on 30 June 1963, starting from pole position. Tony Maggs finished second for Cooper-Climax, with Graham Hill completing the podium for BRM.
| Pos | Grid | Driver | Team | Laps | Time / Status | Pts | FL |
|---|---|---|---|---|---|---|---|
| 1 | 1 | Jim ClarkCLA | Lotus-Climax | 53 | 2:10:54.3 | 9 | |
| 2 | 8 | Tony MaggsMAG | Cooper-Climax | 53 | +1:04.9 | 6 | |
| 3 | 2 | Graham HillHIL | BRM | 53 | +1:13.9 | 0 | |
| 4 | 5 | Jack BrabhamBRA | Brabham | 53 | +2:15.2 | 3 | |
| 5 | 3 | Dan GurneyGUR | Brabham | 53 | +2:33.4 | 2 | |
| 6 | 10 | Jo SiffertSIF | Lotus-BRM | 52 | +1 Lap | 1 | |
| 7 | 17 | Chris AmonAMO | Lola | 51 | +2 Laps | 0 | |
| 8 | 15 | Maurice TrintignantTRI | Lotus-Climax | 50 | +3 Laps | 0 | |
| 9 | 9 | Innes IrelandIRE | BRP | 49 | +4 Laps | 0 | |
| 10 | 21 | Lorenzo BandiniBAN | BRM | 45 | +8 Laps | 0 | |
| 11 | 18 | Jim HallHAL | Lotus-BRM | 45 | +8 Laps | 0 | |
| 12 | 6 | Bruce McLarenMCL | Cooper-Climax | 42 | Ignition | 0 | |
| 13 | 7 | Trevor TaylorTAY | Lotus-Climax | 41 | Suspension | 0 | |
| N | 13 | Phil HillHIL | Lotus-BRM | 34 | Not classified | 0 | |
| N | 11 | Jo BonnierBON | Cooper-Climax | 32 | Not classified | 0 | |
| R | 19 | Masten GregoryGRE | Lotus-BRM | 30 | Gearbox | 0 | |
| R | 4 | John SurteesSUR | Ferrari | 12 | Fuel pump | 0 | |
| R | 20 | Tony SettemberSET | Scirocco | 5 | Wheel bearing | 0 | |
| R | 12 | Richie GintherGIN | BRM | 4 | Radiator | 0 | |
| W | 0 | Ludovico ScarfiottiSCA | Ferrari | 0 | Withdrew | 0 | |
| W | 0 | Peter ArundellARU | Lotus-Climax | 0 | Withdrew | 0 | |
| W | 0 | Giancarlo BaghettiBAG | ATS | 0 | Withdrew | 0 | |
| W | 0 | Ian BurgessBUR | Scirocco | 0 | Withdrew | 0 | |
| W | 0 | Nasif EstéfanoEST | De Tomaso | 0 | Withdrew | 0 |