Partly because they are young business school graduates and partly because getting a driver’s license here is so difficult and expensive that it has inspired books on the subject, Mr. Chartier and Mr. Gaignault have become minor celebrities. Various experts say their struggle highlights how the myriad rules governing driving schools — and 36 other highly regulated professions — stifle competition and inflate prices in France.

The rules set up barriers to newcomers, sometimes indirectly. Lowering them has become a critical test of France’s willingness to confront its declining competitiveness and the drain of its young people to London and other more flexible places from a country where protecting entrenched interests has always ranked higher, politically and culturally, than innovation.

Now, however, with France’s economy faltering and the Socialist government desperate to do something to revive its popularity, some experts expect that President François Hollande’s administration may finally take steps to tear down the tangle of rules that keep competition — and many young people — out of so many sectors of the economy.

But there has been scant progress so far. In the case of driving schools, the government offers only a limited number of exams each year, and these are doled out to the driving schools depending on their success rate the year before. That fact alone gives the old guard a virtual monopoly, according to Gaspard Koenig, who wrote a book on his own (failed) efforts to get a driver’s license here, despite having graduated from one of France’s most elite universities.

“The system is absurd,” said Mr. Koenig, who was a speechwriter for Christine Lagarde when she was the French finance minister. “You are begging to get into the classes. You are getting shouted at by these teachers. It is humiliating.” Mr. Koenig finally got his license in London.