Hingis at least reached two finals in Paris. But youth, a slight arrogance and nerves betrayed her each time.
In 1997, she handed victory to Croatian Iva Majoli, who has since sunk in the world rankings, because of overconfidence.
Last year she failed again, outwitted, outclassed and outplayed by the player she would so much like to emulate -- Steffi Graf.
Given her youth and talent, her skill on clay too, there is little doubt that the 19-year-old Swiss should one day win at Roland Garros.
This could be the year for Hingis, despite a foot injury which forced her out of the Italian Open last week.
Graf has retired, the Williams sisters have barely played lately and three-times winner Arantxa Sanchez Vicario seems way past her best this season.
As for American Lindsay Davenport, Hingis's arch-rival in recent months, she was also injured recently and seems, like Sampras, to suffer from a cultural handicap in Paris.
LAME AND CLUMSY
Both Wimbledon champions could again be picked as favourites on the London grass later in June but their serve and volley games, their power and natural elegance on fast surfaces often look lame and clumsy on the red stuff.
Like Sampras, Davenport has had to be content with reaching the last four on the Parisian clay once and even a final looks unlikely again this year.
Five Frenchwomen will be seeded this year and all will be looking for a fine result with Mary Pierce again her country's best hope.
Sampras's Parisian career has looked so hopeless that there is no reason to believe he can break the jinx on his 11th attempt.
The American has reached the semifinals only once and the last eight only four times, losing much more regularly in the second round.
If the sun shines, if balls are fast, if he is fit, then maybe...but his recent performances on clay have been disheartening as he has won only a single match on the surface this season.
``I'm still optimistic but losing these matches doesn't help my confidence. My main goal is getting my game ready for the French Open,'' he said at the World Team Cup in Duesseldorf.
But even he does not seem to really believe he can make it.
UNIQUE RECORD
``It would be the most unbelievable thing to happen. To win that tournament in which I've never done well...for a unique record, it would be crazy,'' he said.
By winning his 13th grand slam title in Paris, Sampras would not only outshine Australian Roy Emerson with whom he shares the current record of 12, he would also join Andre Agassi as the only player to win all four grand slam events on different surfaces.
Agassi achieved the feat last year by winning at Roland Garros on his way to his best ever season.
The American will be the crowd's favourite for sure, even though many players look, on paper, quite as capable as him of winning in Paris.
Brazil's Gustavo Kuerten has never been in such brilliant form. The 1997 champion won in Hamburg and reached the final in Rome a week earlier. He is rightfully considered the best claycourt player in the game.
But fast-improving Swede Magnus Norman, the leader of the 2000 Champions Race thanks to his victory in Rome, and Russian sensation Marat Safin, winner of two claycourt tournaments this season, will hope to crown their current form with a first major title.
Injuries might also hold the key to victory this year, as they do so often in modern tennis.
Health problems have blurred the true hierarchy this season in both the men's and the women's game and it will be intriguing to find out the real form of Venus and Serena Williams, Australian Pat Rafter, Russian Yevgeny Kafelnikov, Spaniard Carlos Moya and Chile's Marcelo Rios.