* Affair has little impact on Hollande's deep unpopularity
* Trierweiler played role of first lady, with big budget (Adds Trierweiler comment)
By Emmanuel Jarry and Leila Abboud
PARIS, Jan 25 (Reuters) - French President Francois Hollande announced his separation from first lady Valerie Trierweiler on Saturday following a media storm over allegations he is having an affair with an actress.
"I wish to make it known that I have ended my partnership with Valerie Trierweiler," he told Agence France Presse news agency.
Hollande sought to put an end to turbulence that began two weeks ago when celebrity magazine Closer published a report that he was having an affair with film actress and Socialist Party supporter Julie Gayet.
Questions over Hollande's personal life - and whether Trierweiler was still first lady - have diverted public attention from a shift the president made this month towards more business-friendly policies aimed at reviving the euro zone's second-biggest economy in the face of high unemployment.
A news conference to unveil the economic plans was overshadowed by questions over Hollande's private life, as was a trip to Rome to meet the pope on Friday.
Announcing the separation, Hollande said he was speaking as an individual and not as head of state since it concerned his private life.
Trierweiler, a 48-year-old arts columnist for weekly magazine Paris Match, was not married to Hollande but they had been together since 2006. She assumed the role of first lady at official functions following his election in May 2012, and like her predecessors, maintained an office with a budget of roughly 20,000 euros per month.
TRIP TO INDIA
Trierweiler was hospitalised for eight days for fatigue after news of the affair broke, and had since been staying in a secluded secondary residence belonging to the president near Versailles. She left the house, known as la Lanterne, on Saturday afternoon, said a person close to the presidency, and would not return.
In her first public statement, Trierweiler thanked the staff of the Elysee presidential palace in a tweet. "I will never forget their devotion, nor the emotion at the time of my departure," she wrote.
Trierweiler was expected to travel to India on Sunday in honour of an anti-hunger charity, and French media reports said she may speak at a news conference there.
Hollande, 59, is the most unpopular president in modern France, according to polls. He has struggled to live up to a promise to get unemployment, currently stuck near 11 percent, firmly on a downward trend.
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.
The reports of Hollande's affair have had little effect on his image and French media largely focused on Closer's unprecedented breach of presidential privacy rather than on the relationship with Gayet.
A poll by Ifop shortly after the magazine report showed that 84 percent of those surveyed had not changed their opinion about Hollande and that 77 percent considered it a private matter.
Trierweiler has been a particularly unpopular first lady, according to a BVA poll. Some 8 percent of respondents had a favourable view of her, compared to 28 percent for Carla Bruni-Sarkozy, the ex-model and pop star wife of Nicolas Sarkozy, and 46 percent for Bernadette Chirac, wife of Jacques Chirac. (Editing by Andrew Roche and James Dalgleish)