The break-up was confirmed on Saturday by the president, who said in a curt statement that he had “ended his partnership” with the 48-year-old journalist.
That came less than three weeks after the tabloid Closer set off a media storm by publishing photos of what it said was Mr Hollande, 59, making nocturnal visits to the apartment of French actress Julie Gayet, 41.
Ms Trierweiler, who spent eight days in hospital after news broke of the alleged affair, was in Mumbai yesterday with the charity Action Against Hunger.
In her first public comments since the scandal, she did not mention the break-up but gave a tongue-in-cheek thank-you to French journalists who crowded the press conference for their “interest in malnutrition”.
Asked about her health, she said: “I feel very well, it feels good to be here. I have the impression I’m being useful for something. Don’t worry about me.”
Ms Trierweiler, a columnist for Paris Match magazine, had been in a relationship with Mr Hollande since 2006.
After his election in May 2012, she assumed the unofficial role of first lady and had an office at the Elysee Palace with a budget of about €20,000 (£16,500) a month, while continuing to write.
News of the president’s alleged affair – which he has neither confirmed nor denied – has not worsened his record-low approval ratings but has distracted attention from a series of business-friendly policies aimed at reviving the economy.
Mr Hollande is due to travel alone to the United States to visit Barack Obama early next month. Allies said his weekend announcement should put an end to the media scrutiny of his personal life.
Still, some have criticised the way in which he announced the break-up, with some politicians and journalists calling him callous in publicly repudiating his partner.
“More like a pink slip [redundancy notice] than a break-up letter,” conservative politician Nathalie Kosciusko-Morizet said.
Asked about her track record as first lady, Ms Trierweiler – who is deeply unpopular with the public, according to opinion polls – said it was not for her to judge.
“I was there for 19 months. It gave me the opportunity to meet new people and maybe even discover a part of myself that I didn’t know existed,” she said.
She said she did not know what her future held, but that she would continue to do humanitarian work. “I think that all together, we can do something, each in his or her own way,” she said. “That’s what I’ll continue to do, whatever happens.”
Meanwhile, a possible diplomatic banana skin has been avoided, after it was confirmed there will be no official roles for political wives and partners at a UK-French summit this week. Mr Hollande is due in Britain on Friday for the event.
“I do not think there is a spouses’ programme, no,” Prime Minister David Cameron’s official spokesman told reporters yesterday.