By Alasdair Sandford
BBC News, Paris
Ms Royal is considered by some to be vague on international affairs
She may have stumbled during the latest test, but Segolene Royal still remains the favourite to be top of the class at the end of term.
The frontrunner to win the nomination as Socialist candidate in the presidential election was judged by some to have been less assured than her two rivals in Tuesday night's final TV debate.
"Royal masters foreign languages badly", read the headline in the free newspaper 20 Minutes.
The paper described the likely Socialist presidential candidate as vague and lightweight on international affairs. Several times, it said, the more experienced Laurent Fabius and Dominique Strauss-Kahn were like professors to Royal's "average student".
The differences were certainly apparent.
Overall, Segolene Royal is seen as having stood up reasonably well to her competitors
By saying "we must talk to everyone" in the Middle East, Segolene Royal favoured a direct dialogue with Hamas. Mr Fabius and Mr Strauss-Kahn spelled out their reservations.
They had no objection to Iran developing its nuclear capability for civil purposes only, whereas Ms Royal opposed all nuclear activity by Tehran.
They were either for or against Turkish entry to the EU; she repeated that the French people should decide one day in a referendum.
'Not best placed'
When Socialist party members vote next week to choose their presidential candidate, Tuesday's debate will probably be forgotten. Overall, Segolene Royal is seen as having stood up reasonably well to her competitors.
Opinion polls show Ms Royal with a substantial lead over her rivals
"Three rounds, no knock-out", said the newspaper Liberation, referring to the three televised debates. It argues that the various blows and counter-blows away from the cameras will prove more decisive.
Dominique Strauss-Kahn said on Wednesday that Segolene Royal was "not the best placed" to win the battle against the expected main candidate from the right, Interior Minister Nicolas Sarkozy.
Opinion polls have suggested the opposite is true, and may influence how some party members vote next week, regardless of their personal stance on Ms Royal.
At least three new polls this week confirm Segolene Royal's substantial lead over her rivals, among Socialist sympathisers.
Two surveys suggest 60% or more would prefer to see her run for the Elysee. But, as Le Parisien newspaper has pointed out, these are the views of party supporters, whereas it is only party members who will cast votes.
Some 66,000 new people have signed up to the party this year. Many have done so on the internet, encouraged to do so by Segolene Royal herself. But at Socialist meetings many new members have revealed themselves to be hostile to the direction she wants to go.
They see her views, such as her calls for a shake-up to the education system and the 35-hour working week, as a betrayal of the Socialist Party's leftist credentials.
Several of those the French call the "elephants", senior Socialist figures rooted in the party's traditions, have fallen away in the presidential race. But behind the scenes, allies of the two-time election loser Lionel Jospin are suspected of preparing a final charge.
"Anyone but Segolene" was how many saw the former prime minister's parting message when he withdrew from the contest. His supporters are hoping that she will fail to win an outright majority next week, forcing a second round of voting. The outcome of that could be unpredictable.
Segolene Royal is into the final straight in the race to become the Socialist presidential candidate. But she has every reason to keep looking over her shoulder.