Clijsters wobbles but beats Barrois in Paris
The Belgian, who won the Australian Open last month, can take the number one spot from the absent Caroline Wozniacki if she reaches the semi-finals at Stade Coubertin - just a short walk from Paris's more celebrated tennis venue Roland Garros.
After losing the first four games against world number 78 Barrois on the hardcourt, the top seed's hopes of such success looked bleak with her serve erratic and forehand often long.
Clijsters pulled herself out of the rut by reeling off a string of winners but a drive volley into the net cost her the first set.
Barrois continued to trouble her more illustrious opponent with a cunning sliced backhand but her confidence gradually drained as Clijsters upped the tempo and lifted the crowd out of their early state of shock.
"In the second set I got it together and in the third set I just tried to keep the pressure on," Clijsters said courtside.
Andrea Petrovic, the sixth seed, also struggled against fellow German Angelique Kerber in a first-round tie before prevailing 7-5 3-6 6-2 while Belgium's Yanina Wickmayer dispatched Elena Vesnina 7-6 6-2 in one hour 35 minutes.
Sofia Arvidsson of Sweden also overcame local hope Alize Cornet in straight sets 6-2 7-6 (5).