In a park by the canal edge in Saint-Denis, Laken Lima sat in a deckchair at an Olympic fan zone watching the taekwondo on a big screen, as tourists and locals mingled in a party atmosphere in this banlieue town on Paris’s northern border.

“I’ve been so pleasantly surprised by the Olympics,” said the 38-year-old local health coach. “It has been magical, we’ve been blown away.” Lima was one of more than 4.5 million people who have flocked to watch giant screens at fan zones and free community events across France over the past two weeks as the country hails these Games as a monumental success.

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The Paris Olympics has broken records not just for ticket sales – 9.4m – but also for TV viewing figures. The opening ceremony was the most-watched TV event in French history, with more than 24 million viewers. France has also exceeded expectations in the medal table – hoping to finish in the top five, thanks to gold medals in sports ranging from fencing and judo to surfing and BMX racing.

But perhaps the biggest victory has been the Olympic feelgood factor. The country is riding high on joy and togetherness after the tense mood around a snap parliament election that was called by Emmanuel Macron just before the Games to try to counter the surging far right, but which has laid bare France’s stark political and class divides. France still does not have a new government after those elections, but the Games appear to have put sticking plaster over the wounds.

More than the beautiful Eiffel Tower backdrops, the Olympic legacy and lasting impact of this feelgood factor will be judged in the Paris banlieue – or suburbs – in places such as Saint-Denis. It is in these neighbourhoods that the only permanent new buildings were constructed – the Olympic village and the aquatics centre. The Games promised to accelerate regeneration in the broader département of Seine-Saint-Denis, one of the poorest in France, whose young, multi-ethnic population has historically faced discrimination but is now seen as one of France’s greatest talent pools, from business startups to sport.

The US stars Pharrell Williams and Snoop Dogg featured in Saint-Denis’s own Olympic flame ceremony to rival the opening ceremony proper. “I cried at that ceremony because I felt that at last people were really seeing us and valuing us for who we are,” said Lima, who was at the fan zone with other entrepreneurs part of a local association, Plaine Commune Promotion.

Leonnel Saffou, the head of a local risk-assessment business, had been at the men’s rugby sevens at the nearby Stade de France for France’s first gold. “It reminded me of France winning the football World Cup in 1998 when, for about a year afterwards, everyone felt happy. I hope these games will have a lasting positive impact.”

Samantha Bimbin, who will be setting up a creche and centre for the elderly in one of the buildings left by the Olympics, said: “The point of honour for us is that the Games have shown the kindness of this place, the notion of living together. Seine-Saint-Denis is a melting pot and the whole of France has benefited from seeing that.”

Many French athletes said their sporting achievements were boosted by what they felt were unprecedented levels of cheering, flag-waving and enthusiasm from home supporters. “Fans were on fire … they were there to lift us and they really helped,” said Lisa Barbelin, who won a bronze in archery. “People were stamping their feet in the stands so much that our bows were shaking,” she told French radio.

Macron’s presidency has shown that it takes more than sporting events to reconcile a nation: in 2018 France won the men’s football World Cup but months later, the gilets jaunes protests saw the biggest anti-government demonstrations in years. This time, many hope the Olympic spirit runs deeper, showing France’s capacity for uniting. “We do have a beautiful country,” said Thierry Henry, now coaching the French men’s Olympic football team. “When we decide to be together, we’re unstoppable, when we know how to unite, we’re good.”

Mathieu Hanotin, the Socialist mayor of Saint-Denis, said: “I’m happy we’ve shown that our country knows how to unite and get together and is ultimately not as divided as has been said. In Saint-Denis we wanted to show, as a legacy of the games, that this town is becoming more and more attractive while also remaining cosmopolitan and multicultural. That’s the proof that the [French] Republic can work: we can progress together with all our differences, and those who call for people to close in on themselves in hatred of others are wrong.”

From the cycling road race winding its way up the cobbled hills of Montmartre as half a million people lined the streets, to the queues for stadiums, one element of surprise good cheer has been the positive image of French police. Just over a year ago, unrest spread across towns in France after the police shooting of Nahel, a 17-year-old boy of Algerian and Moroccan descent, at a traffic stop outside Paris. The previous year, police were criticised for tear-gassing Liverpool supporters amid the chaotic organisation of the Champions League final at the Stade de France.

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Now, with around 30,000 police on duty every day of the Games, the relationship between officers and the public has seemed more positive than it has been for years – many posed smiling, or even dancing, in the streets with spectators. The brass band of the police force’s Garde républicaine not only performed with the pop star Aya Nakamura for the opening ceremony, in a strong message of togetherness for France, but also delivered a rousing rendition of Freed from Desire, an unofficial anthem of the Paris Games, amid spectators in Montmartre.

France’s Anaïs Bourgoin, who ran the 800m and has served in the police, said: “Yes, it’s true that I ran after thieves at Porte de Saint Ouen and now I’m running at the Stade de France in the Games. I hope they’ll see me and understand why I always caught them.”

The challenge now for France is hanging on to the positivity. “The message of fraternity and humanism overcame everything else,” the Paris mayor Anne Hidalgo told French TV. “I hope that continues. It’s up to us politicians to make this moment last.”