PARIS — French President Francois Hollande conceded Tuesday that he is going through “painful moments” with his companion, who was hospitalized after a magazine reported that he is secretly having an affair with a movie actress.

But the Socialist Hollande, who has some of the lowest approval ratings of a French leader, sidestepped specifics about his personal life and tried to devote his annual presidential news conference to his plan for reviving France’s struggling economy.

Hollande’s partner, journalist Valerie Trierweiler, has been hospitalized since Friday, when the tabloid-style magazine Closer published photos it said proved Hollande’s liaison with actress Julie Gayet around the corner from the presidential Elysee Palace.

Hollande said Trierweiler “is resting” but insisted that the packed news conference was not the place to discuss the issue.

He did not deny or confirm the Closer report, but his announcement Tuesday of economic measures meant to encourage hiring was overshadowed by the scandal.

Hollande has four children with another leading Socialist politician, Segolene Royal. He left Royal for Trierweiler, whom he has lived with since 2007.