(Adds details on poll, background)
PARIS, Jan 24 (Reuters) - France's first lady Valerie Trierweiler is returning to charity work with a trip to India, an anti-hunger group said, two weeks after she was hospitalised following a report that Francois Hollande had an affair with an actress.
Trierweiler, 48, spent a week in hospital to recover from shock and another week resting in a presidential residence near Versailles after the report was published.
Celebrity magazine Closer this month published what it said were images of Hollande making a nocturnal visit to French movie actress Julie Gayet's apartment in Paris.
The head of Action contre la Faim, Valerie Daher, said Trierweiler would go ahead with a long planned private trip to Mumbai on Monday to support the French charity against hunger.
"She's been through a difficult period and is very tired. She feels better, at least enough to make the trip, although we had to cut it short," Daher said on BFM TV.
Hollande has acknowledged the turbulence in his private life and pledged to clarify Trierweiler's status before a trip to the United States scheduled for Feb. 9, but has steered clear of journalists' questions about the alleged affair.
Trierweiler has been Hollande's partner since 2006.
The president was holding his first meeting with Pope Francis in Rome on Friday, the same day a poll showed two-thirds of people surveyed believed that the focus on his alleged affair had been bad for the image of the traditionally Roman Catholic country.
At home, the storm has diverted public attention from a shift Hollande has made this month towards more business-friendly policies, which he hopes will revive the euro zone's second-biggest economy in the face of stubbornly high unemployment.
Hollande, 59, is the most unpopular president in modern France, according to polls, as he has struggled to live up to a promise to get unemployment, currently stuck near 11 percent, firmly on a downward trend.
Trierweiler, who was a reporter for glossy weekly magazine Paris Match and has continued there as an arts columnist, is not married to Hollande but assumed the role of first lady at official functions following his election in May 2012.
He has four children from a previous relationship with Segolene Royal, a senior member of his Socialist Party and a 2007 presidential candidate. Royal announced their separation just after she lost the 2007 election to Nicolas Sarkozy. (Reporting by Gerard Bon; Writing by Leigh Thomas; Editing by Alison Williams and Sonya Hepinstall)