PARIS — Almost from the moment Venus and Serena Williams appeared on the Grand Slam scene in the late 1990s, they’ve been winning titles and transcending tennis, becoming red-carpet celebrities as much as sports stars.

Every so often, like all elite athletes, they’ve heard questions about whether their best days were behind them, whether health problems or off-court distractions were taking their toll. And each time, it seemed, one or the other — or sometimes, amazingly, both — would promptly reach a major final, as if to say, “Hey, don’t count us out yet.”

Now that each is past her 30th birthday, and big victories are less frequent than ever, those questions are bound to get more persistent, especially after this week. The 2012 French Open has been the worst Grand Slam tournament in Williams family history, the first of the 43 that both entered at which neither reached the third round.

Venus lost 6-2, 6-3 in the second round Wednesday at Roland Garros, barely providing any resistance against Agnieszka Radwanska of Poland, who might be seeded No. 3 but never has been past the quarterfinals at a major tournament.

Serena, meanwhile, lost 4-6, 7-6 (5), 6-3 in the first round Tuesday to Virginie Razzano of France, a woman who is ranked 111th and never has made it beyond the fourth round at a major tournament. Making it more surprising: Serena was two points from victory nine times but couldn’t close the deal.