The RE60 followed the RE50 — itself a winless season — at a time when the Renault works team was in serious structural difficulty. Several key engineers had departed, including lead chassis designer Michel Têtu, and the entire employment structure had been reshuffled. The team retained drivers Patrick Tambay and Derek Warwick from 1984, and the RE60 was the only Renault Formula One car ever run on Goodyear tyres, having previously used Michelin.
Before the season, Niki Lauda had signed an initial letter of intent to leave McLaren and join Renault for 1985, but the agreement was not implemented and Lauda remained at the team where he had won his third World Championship.
The RE60 was an evolution of the RE50 but proved to be markedly inferior from its first pre-season tests. During testing at the Jacarepaguá circuit in Rio de Janeiro, Warwick found the car to be three and a half seconds slower than the previous year's RE50 and later described it as "impossible to drive." A modified specification, designated RE60B, was introduced at the French Grand Prix mid-season but failed to generate any improvement in results.
The best results achieved by the RE60 were two third-place finishes for Tambay, at the Portuguese Grand Prix and the San Marino Grand Prix — the second and third races of the season. These proved to be the final podiums for the factory Renault team in their original works guise. Warwick scored no podiums and his Formula One career trajectory, already compromised by a decision to stay at Renault rather than join Williams for 1985, never recovered from the difficult season.
The scale of the RE60's failure was underlined by the performance of customer teams using the same Renault turbocharged V6 engine. Lotus, with Ayrton Senna and Elio de Angelis, finished fourth in the Constructors' Championship with 71 points and three race wins. Ligier, another French team, finished sixth with more points than the factory Renault outfit. Renault themselves finished seventh with just 16 points, outscored even by Tyrrell, who had only adopted Renault engines partway through the season. Warwick, reflecting on his decision to stay at Renault rather than join Williams, later admitted regret: the Williams FW10-Honda won four races in 1985, including Nigel Mansell's first two Formula One victories.
The Renault team boycotted the 1985 South African Grand Prix, along with the other French Formula One teams, in lockstep with the French government's protest against apartheid in South Africa.
Renault withdrew from Formula One as a constructor at the end of 1985, having concluded that the costs of running a works team could not be justified by the returns in either technology transfer or public relations — particularly after the team had been consistently outperformed by Lotus using an identical engine. The Renault V6 turbo engine continued to be supplied to customer teams including Lotus in 1986, and Renault subsequently became an engine supplier with naturally aspirated V10 units throughout the 1990s.
The Renault name returned to Formula One as a constructor only after the purchase and rebadging of the Benetton team at the end of 2001. In that context, the RE60 remains the last car of Renault's pioneering first era — the period in which they introduced turbocharged engines to the sport and, despite multiple near-misses, never secured a drivers' or constructors' world championship.