Despite a long career in French politics, her image as a fresh face, strong on traditional values and ready to listen to citizens' concerns has played well with a public tired of leaders seen as more elitist.
Strauss-Kahn, 57, a former finance minister running as a social democrat and Fabius, 60, a prime minister in the 1980s now positioned on the party's left wing, have trailed behind her.
A poll in the weekly Le Point on Thursday put Royal and Sarkozy level if they face each other in the decisive round of voting next year.
The outcome of Thursday's poll is unpredictable because opinion polls have counted "socialist sympathisers" rather than the 219,000 actual party members who will vote.
The US-style poll of party members is a first in French politics, where leadership candidates have traditionally emerged after backroom deals between party heavyweights.
Whoever wins will have the task of uniting a party still scarred from the 2002 election when Lionel Jospin went out in the first round after trailing far-right candidate Jean-Marie Le Pen.
Six hours of voting begins at 1500 GMT and a result is due on Friday morning.
If no candidate wins an absolute majority in the first round, a second will be held on November 23, a prospect Royal's supporters worry could damage her image and slow her momentum before the confrontation with the right next year.