"We've got a system that seems to be delivering. It's driving the French mad," Cameron told BBC radio in an interview.
"I did an interview with French television yesterday and they virtually accused us of cheating.
"I think they found the Union Jacks on the Champs Elysees a bit hard to take," he said, referring to Briton Bradley Wiggins' victory last month in the Tour de France.
In the interview with France 2 television broadcast on Wednesday evening, Cameron laughed off French suspicions about the hosts' stellar success in the velodrome at the London Games.
"The French should know our secret because you make our wheels," Cameron said, referring to the French manufacturer Mavic.
"You know they're round. They go fast because they pedal hard," he added, laughing.
The British team took seven out of the 10 titles in the velodrome, prompting French technical director Isabelle Gautheron to say she was "perplexed" by the success and leading to calls on social networking sites of cheating.
A majority (70 percent) of 50,000 people who responded to a question in the sports newspaper L'Equipe about whether the British were "tainted by cheating" also said they suspected foul play.
But Cameron said: "I think that it's unfair to think that just because someone wins you have to doubt it. The first reaction should be to say, 'well done, congratulations'.
"I understand that for France, which is a great cycling nation, that it must be a bit hard to take but we have really done well and I'm sure that if France had won we would have been happy for you," he added, still smiling.
Britain's success has been seen as the perfect response to French President Francois Hollande's quip early in the Games that the British had rolled out the red carpet for French winners after early successes, notably in the pool.
At the time, France were ahead of Britain in the medal table but the host nation has more than made up ground and now occupies third spot behind China and the United States with 48 medals, including 22 gold.
France has 28, including eight gold, and is sixth in the table.