Mr Strauss-Kahn abandoned plans to run after he was accused of rape last year.
Both Mr Fabius and Mr Strauss-Kahn sent messages of congratulation soon after their defeat.
ECONOMIST: S��gol��ne Royal ushers in a new era of French politics
Some, such as Mr Strauss-Kahn, are less interventionist than others, such as Ms Aubry.
Every couple of months Mr Strauss-Kahn drops into Paris, lunching and dining with the right people.
Yet Mr Hollande's score is shared with Mr Strauss-Kahn and a handful of others.
Mr Strauss-Kahn's twin search for legitimacy and relevance will soon be put to the test.
When Mr Strauss declared he was unworried, Mr Fletcher did not impose his view.
Mr Strauss-Kahn's predecessor, Rodrigo de Rato, left the post after only three years, for personal reasons.
More important in the short term is the political fall-out from Mr Strauss-Kahn's departure.
There is, however, a different reason to be worried about the loss of Mr Strauss-Kahn.
Mr Strauss-Kahn's easy charm may not be enough to keep them happy when the euro-11 gets going.
Mr Sarkozy's UMP party has previously denied any allegations it was involved in a plot against Mr Strauss-Kahn.
Mr Strauss-Kahn had arranged for a friend to examine the phone upon his planned arrival back in Paris.
Ms Banon's lawyer, David Koubbi, said this week that she was intending to press charges against Mr Strauss-Kahn.
For Mr Strauss-Kahn, it is awkward to be yoked to a policy platform so far to his left.
Mr Strauss-Kahn was able to survive an affair with a subordinate working as an IMF economist in 2008.
There were already fears that Mr Strauss-Kahn's presidential ambitions led the fund to be too soft on Europe.
Most notably in global food prices, Mr Strauss-Kahn warned this food inflation could undermine recent gains in reducing poverty.
Under this scenario, Mr Hollande could stay as party head even if Mr Strauss-Kahn, say, became the official candidate.
But the timing may not be so propitious for Mr Strauss-Kahn this time.
Despite a spell as trade minister in the previous Socialist government, Mr Strauss-Kahn has not been a household name.
So Mr Strauss-Kahn now predicts 3% growth next year, up from an expected 2.2% this year and 1.5% last.
Mr Strauss-Kahn, in her view, represents the elite that she maintains has lost touch with ordinary French working people.
Ms Banon's lawyer, David Koubbi, said he had sent a complaint against Mr Strauss-Kahn to Paris prosecutors on Tuesday afternoon.
Speaking at the IMF's headquarters in Washington, Mr Strauss-Kahn also described the current economic situation as between "ice and fire".
Once the police had arrested Mr Strauss-Kahn, he was held in the infamous Ryker's Island jail, notorious for gang violence.
Mr Strauss-Kahn is unlikely to want to give up his plum job to return to face a grubby nomination contest.
The Independent says Mr Strauss-Kahn, who denies the claims, is a figure of formidable talents as well as flaws.
It will not boost his poll ratings, but he will face candidates with nothing like the standing of Mr Strauss-Kahn.
But Mr Strauss-Kahn acknowledged in April 2011, before the Sofitel incident, that he had a potential political problem over his womanising.
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