| Pos. | No. | Driver | Entrant | Constructor | Time | Grid |
|---|---|---|---|---|---|---|
| 1 | 6 | Bruce McLaren | Cooper Car Company | Cooper-Climax T60 | 2.02:30.2 | 4 |
| 2 | 2 | Graham Hill | Owen Racing Organisation | BRM P57-8 | + 8.0 s | 2 |
| 3 | 30 | Innes Ireland | UDT-Laystall Racing Team | Lotus-Climax 24 | + 1:36.3 s | 7 |
| 4 | 22 | Jack Brabham | Brabham Racing Organisation | Lotus-Climax 24 | + 2:03.6 s | 5 |
| 5 | 24 | Maurice Trintignant | Rob Walker Racing Team | Lotus-Climax 24 | 49 laps | 8 |
| 6 | 28 | Roy Salvadori | Bowmaker Racing Team | Lola-Climax Mk4 | 49 laps | 10 |
| 7 | 46 | Carel Godin de Beaufort | Ecurie Maarsbergen | Porsche 718 | 48 laps | 11 |
| 8 | 36 | Jo Bonnier | Scuderia Serenissima | Porsche 718 | 48 laps | 14 |
| 9 | 40 | Jo Siffert | Ecurie Filipinetti | Lotus-Climax 21 | 46 laps | 15 |
| 10 | 34 | Jack Lewis | Ecurie Galloise | Cooper-Climax | 46 laps | 18 |
| 11 | 44 | Ian Burgess | Anglo-American Equipe | Cooper-Climax Special (Aiden Cooper) | 45 laps | 17 |
| Ret | 14 | Peter Arundell Jim Clark |
Team Lotus | Lotus-BRM 24 | Out of fuel | 13 |
| Ret | 4 | Richie Ginther | Owen Racing Organisation | BRM P57-8 | Gearbox | 9 |
| Ret | 26 | John Surtees | Bowmaker Racing Team | Lola-Climax Mk4 | Valve spring | 3 |
| Ret | 38 | Carlo Abate | Scuderia Serenissima | Lotus-Climax 18/21 | Accident | 20 |
| Ret | 8 | Tony Maggs | Cooper Car Company | Cooper-Climax T55 | Oil pressure | 16 |
| Ret | 10 | Jim Clark | Team Lotus | Lotus-Climax 25 | Header tank | 1 |
| Ret | 12 | Trevor Taylor | Team Lotus | Lotus-Climax 24 | Accident | 12 |
| Ret | 42 | Tony Shelly | John Dalton | Lotus-Climax 18/21 | Head gasket | 19 |
| Ret | 32 | Masten Gregory | UDT-Laystall Racing Team | Lotus-BRM 24 | Accident on grid | 6 |
| WD | 16 | Giancarlo Baghetti | Scuderia Ferrari | Ferrari 156 | Strike in Italy | - |
| WD | 18 | Lorenzo Bandini | Scuderia Ferrari | Ferrari 156 | Strike in Italy | - |
| WD | 18 | Ricardo Rodríguez | Scuderia Ferrari | Ferrari 156 | Strike in Italy | - |
| WD | 20 | Willy Mairesse | Scuderia Ferrari | Ferrari 156 | Strike in Italy | - |
| WD | 42 | Tony Marsh | Tony Marsh | BRM P48/57 | Car not ready | - |
Date: July 1, 1962
Official Name: III Grand Prix de Reims
Circuit: Reims-Gueux
Location: Reims
Circuit Length: 8.3 km
Number of Laps: 50
Race Distance: 415 km
Pole Position: Jim Clark, Lotus-Climax, 2:22.9
Fastest Lap: Graham Hill, BRM, 2:24.0