In the table of winners and losers of the Olympic Games, Paris has declared it has snatched gold in a victory over defeatism and doomsaying. As the greatest sporting show on Earth winds up for another four years, the decision to showcase the French capital and its most iconic monuments is the gamble that paid off despite a damp and shaky start.

The rainy and controversial opening ceremony was quickly forgotten as visitors and viewers watched volleyball against the backdrop of the Eiffel tower, fencing under the massive glass-barrelled roof and art nouveau decor of the Grand Palais and triathlon races in the river Seine.

Pierre Rabadan, Paris deputy mayor in charge of sports and the Olympics, said even the sceptics had been forced to concede. “It’s been a huge success. An extraordinary and exceptional moment that has reinforced the image of Paris,” he said. “I’ve had people, Parisians, French, visitors, who admitted they didn’t think we could do it, come and say merci; thank you. It’s given us all enormous satisfaction.”

More importantly, he said, the Games have not only changed minds but will also leave a lasting legacy in the city and its suburbs long after the athletes and visitors have gone home.

Today, thanks to work accelerated for the Games, Line 14 of the Métro links the centre of Paris with Orly airport in the south, and Saint-Denis in Seine-Saint-Denis, France’s poorest and most unloved banlieue, in the north. For many living in Seine-Saint-Denis in the shadow of the Stade de France, conversations interrupted by roars from the Olympic crowds have served to reinforce a profound sense of exclusion over the last fortnight.

“The Olympic Games are for the rich, not for us,” Farid Khelifi, 61, who described himself as a “taxi artisan”, said. “Have you seen the price of the tickets? It’s far too expensive for people here. Even those who have jobs are on low salaries.”

Carmel Lelo, 45, who works in a medical laboratory, added: “We were the forgotten people of the republic before the Games and we will be forgotten after the Games. We will be back in the shadows again.” Local politicians, like Rabadan, and organisations hope they will be proved wrong.

Tristan Bodin, of Plaine Commune, a public body formed by nine northern banlieue towns, said about 80% percent of investment for the Games was spent in Seine-Saint-Denis, about €4.5bn on permanent structures.

As well as renovations to the Stade de France, it now boasts a new aquatics centre as well as the Olympic and media villages, some of which is destined to become hundreds of local authority homes.

“We’ve come out of this well,” Bodin said. “Although some of it is temporary, there are new sports facilities, especially swimming pools, that will become public after the Games. This is important in a department where half the children can’t swim at the age of 11. It’s not just new projects but the speeding up of existing ones.”

Florent Monnac, 33, who moved to Saint-Denis, the most populated town in Seine-Saint-Denis, two years ago, said: “It’s very French to complain, but the Games can only have a positive effect here, now, in five years, in 10 years and anyone who thinks they aren’t good for the town needs their head examined. Many activities and events are organised here and when the visitors have gone we will be left with the sports facilities.”

Patricia Nex, 62, a retired secretary, was also optimistic the Games would have a lasting legacy for the area. “I don’t know if it will change Seine-Saint-Denis in the long term but I’d like to be optimistic. They have promised us more shops and facilities,” she said.

Lelo, however, was sceptical that locals will see any long-term benefits. “Perhaps public services like transport will improve, but most of the housing will be sold privately I’m sure, and people will profit from the Games to make us pay more.”

Affi, 40, a self-employed business adviser, agreed: “I think all we will be left with in the long term are memories of the Games being held here.”

For the 10 years she has been in charge of city hall, Anne Hidalgo, the Socialist mayor, has made “urban transformation” a priority. On being named host for the Olympics in 2015, the authority made a commitment to use existing infrastructures and eco-friendly temporary venues where possible and accelerate the projects already planned or under way.

It has seen positive results, among them a seemingly impossible ambition to make the Seine swimmable and a major makeover of the rundown Porte de la Chapelle, the main northern gateway into the city, including an 8,000-seat arena and gymnasiums.

Just over Paris’s motorway ring road, the péripherique, from Porte de la Chapelle, Seine-Saint-Denis is one of the suburbs in the capital’s “little crown” and part of the Métropole du Grand Paris, an inter-municipal body fostering cooperation between 131 local councils, representing 7 million people.

This is the mythical 93 or neuf-trois, the historically working-class immigrant area that has been the focal point of France’s wider social fracture and public fears. When Parisians talk disparagingly of le banlieue they are referring to Seine-Saint-Denis.

Once the resting place of French royals – it boasts the royal basilica of St Denis, the patron saint of France and Paris, monuments and cultural sites, parks and canals – Seine-Saint-Denis has been a dumping ground for industries, activities and people considered undesirable in the city intra muros for the last century, creating a seemingly unbreakable cycle of poverty, exclusion, disaffected youth, unemployment and crime.

Since riots in 2005 and terror attacks in and around Paris in 2015, after which it was claimed more than 60 locals had left to join Islamist organisations, the department has been regarded as a hotbed of civil unrest and religious extremism.

An estimated 30% of the 1.7 million population are immigrants, asylum seekers or undocumented workers and there are regular clashes between youths and police with accusations of heavy-handed policing and racism.

Almost all the young people approached did not want to speak. Outside the new Saint-Denis-Pleyel Métro station, the terminus for Line 14, one woman, who did not want to be named, told the Observer: “We will see in 2025 if all the things reserved for the Olympic Games are open to the public. Psychologically, people feel they have been forgotten, have no dignity and are despised by society. They feel relegated. So we hope the Games will have concrete repercussions.”

Rabadan said: “When Paris bid for the Games, Anne Hidalgo wanted the material heritage to be in Seine-Saint-Denis department quite simply because it is the poorest in France and with the youngest population.

“People said we were mad to be sending foreign tourists there into an area where there are so many poor people, that they would be attacked, that it would be a terrible image of France, but we have shown them they were wrong. I don’t have a crystal ball and tthe Games will not change everything overnight but there will be a concrete legacy.”

Hidalgo has said she would like iconic features of Paris 2024 – the giant balloon lifting the Olympic cauldron and the 10 “golden” statues of women who have left their mark on French history – to find a permanent home in Paris, along with the Olympic rings on the Eiffel tower, though the latter seems unlikely.

Rabadan hopes the legacy of the 2024 Games will be far reaching – encouraging greater investment in sport in France and a new model for future Olympics. “We have created an extraordinary and exceptional moment. We have created a Games in an environment that has no equivalent in the world,” he said.

“The Games have changed Paris and Paris has changed the Games.”