François Hollande might have thought the eurozone crisis and the question of France's spiralling public debt would have knocked his love life off the front pages.

But that underestimates the media's thirst for an extraordinary public-private triangle, which shows no sign of abating.

Headlines were made around the world when Valérie Trierweiler, a journalist and France's first lady, used Twitter to take a dig at the president's famous politician ex-partner, Ségolène Royal, during the hugely important parliamentary election campaign. An angry Royal was subsequently defeated and the curtain was raised on the seemingly rancorous backdrop to the presidential relationships, causing much embarrassment to Hollande.

But the Trierweiler v Royal saga continued this week as Royal told a magazine of her hurt feelings; Trierweiler told a paper through an unnamed "friend" that she had made an "error"; and French satirists leapt on it. The French equivalent of Spitting Image, Les Guignols, ran the latest in a regular series of sketches of a buffoon-like Hollande caught between sparring, jealous partners in what promises to be the longest-running joke of the presidency.

Magazines have rushed to put Trierweiler on the cover, perhaps hoping for the same boost in sales as Cecilia Sarkozy brought during the worst moments of her ups and downs with the former president Nicolas Sarkozy. "Who's the boss?" asks the cover of the news weekly L'Express under a picture of Hollande and Trierweiler. "Alone versus everyone: How she can bounce back," headlined Elle magazine with a Trierweiler cover photo.

The latest element in the mix is Trierweiler's new book, François Hollande, President: 400 Days Behind the Scenes of a Victory, published on Friday/today, in which she gives her take on Hollande's presidential campaign in the form of personal and sometimes acerbic picture captions for a photo-essay on Hollande's fight to lead France.

Trierweiler, who covered the Socialist party for Paris Match and began a relationship with Hollande two years before Royal officially announced the couple's split in 2007, has vowed to keep working as a journalist. But the book is her first written account of a campaign in which she was ever present.

Her contributions read like a campaign diary: "He takes me in his arms, safe from view. I cry, he laughs," she writes of the night he won the Socialist primary race.

But the caption that has inevitably dominated media coverage is about Hollande's April rally in Rennes with his ex, Royal – their first political rally together of the campaign. Trierweiler writes: "Ah, the Rennes rally! Or rather the Hollande-Royal rally. In short, the François-Ségolène reunion. Lots has been written since the start of the week, the photographers are here en masse. 'Will they kiss or shake hands?' Those are the crucial questions my fellow journalists are asking. Yes, the man I love had a woman before me. And she happens to have been a presidential candidate. I have to live with it."

Just before the book came out, Royal told the news weekly Le Point of her anger at Trierweiler's surprise tweet of support and message of good luck for a rival dissident candidate who went on to beat her in La Rochelle. "It's an inversion of roles. It was me whose family was wrecked," Royal said, adding that she was the one who might be expected to bear a grudge after Hollande left her for Trierweiler.

Royal felt Trierweiler's relationship with Hollande was part of the reason she did not get full support from him and some in the Socialist party during her presidential bid in 2007. She criticised Paris Match magazine for allowing Trierweiler to keep writing about Hollande when she had begun a relationship with him. "In an Anglo-Saxon country, it would have been the sack that very day," she said, adding that Paris Match and its owner, Arnaud Lagardère, a friend of Sarkozy, and Sarkozy himself, were happy to see Royal "weakened".

Trierweiler did not go to the G20 in Mexico with Hollande and has kept a low profile after the prime minister, Jean-Marc Ayrault, advised greater "discretion". This week, the newspaper Le Parisien reported that she had told "a friend" the tweet was an "error" and she was upset about the negative image that resulted from it. An unnamed source close to Hollande told the paper the president was "furious" and it was clear that "this could never happen again".