I'm afraid I don't know the manufacturer of the gum
I realise that this is a 'know it or you don't' question, and so I will give a bit of a clue by describing the race in general.
The year is one in which there were two other fairly famous Grands Prix (plus many less well-known ones, of course), one of which was the Monaco GP, and the other was the Tripoli GP.
The two drivers involved were two of the best in the world at the time. In fact, one of them could arguably be the greatest driver in motor racing history. The decision by the team to pair them up at Le Mans caused much excitement as both would want to be the number one driver, and they showed it in the build up to the race.
In the race, this car was looking very strong in the opening stages but started to develop problems with the car, one of which was a petrol leak and caused the chewing gum fix. In the end, the driver who I have described as one of the greatest ever had to make up one lap on the leader, and managed to catch him on the final lap, during which there were three lead changes between the two lead cars and the car with the chewing gum was victorious.
This driver would go on to have a famous win at the German Grand Prix two years later, one of the greatest ever race drives.
The other driver would race one season in Formula 1, drive for two teams, and briefly lead the Belgian Grand Prix.
The manufacturer has won a driver’s championship in Formula 1, a couple of decades (approximately) after this Le Mans win.