Dimitri Payet is sitting inside the Olympic Stadium and peering around the vast bowl that will become West Ham United’s home next summer, drinking it in, wondering how it will look when the finishing touches are applied. The £272m transformation into a ground that can house a football club is ongoing, builders are milling around in the background and there are so many hard hats and hi-vis jackets on show it would not be a surprise if a politician materialised and started talking about legacy.

West Ham, whose move to the stadium has not been welcomed warmly by those who argue that taxpayers are getting a raw deal, are keen to stress this is not the final product and what they call its Westhamification will be put on hold when the Rugby World Cup starts next month. The stadium is hosting five matches and there is a dress rehearsal on Saturday afternoon, a warm-up match between Samoa and Barbarians.

All things being, well, better than they are for West Ham at the moment, Payet will be one of the stadium’s star attractions next season. Although leaving Upton Park is an emotional wrench, the belief is that the revenue from a 54,000-seat stadium will allow West Ham to compete financially with the biggest clubs in England. People will pay to watch Payet, whose tally of 17 assists for Marseille last season was the fourth highest in any major European league. The midfielder also made 134 chances, more than Kevin De Bruyne, more than Eden Hazard and more than Lionel Messi.

The more pessimistic view is that when West Ham play their first competitive match at the Olympic Stadium, they will be a Championship side. Relegation is a possibility if Slaven Bilic’s side do not improve quickly. Since winning at Arsenal in their opening match, West Ham have lost at home to Bournemouth and Leicester City. They visit Liverpool on Saturday afternoon and need attacking reinforcements before the transfer window shuts on Tuesday.

At least Payet has caught the eye, creating Cheikhou Kouyaté’s goal against Arsenal and scoring against Leicester. His impish dribbling and ability to pick out a pass could make the difference for West Ham. When Payet is weaving his magic there is hope for the Londoners, and he knows what Bilic wants from him. “The same as at Marseille,” Payet says. “To be present, to organise the game.”

The former France manager Raymond Domenech believes that Payet is too good to play for West Ham. Marseille could not afford to turn down West Ham’s £10.7m offer and criticised the player and his agent for making “reckless demands” during contract negotiations. Payet was left out of the French squad by Didier Deschamps on Thursday. The timing is not ideal: France are hosting next summer’s European Championship.

Dimitri Payet in action for West Ham Photograph: Steve Bardens/Getty Images

Yet Payet has always been single-minded. Perhaps it comes from growing up on Réunion in the Indian Ocean.

The former Newcastle United winger Laurent Robert was also from the French island and, it is safe to say, he could be difficult to manage. “We are mentally quite strong,” Payet says. He began his career there, before joining Le Havre when he was 12. It did not go well. His focus was questioned and he returned to Réunion four years later. Still, it was a fine place to live. “Not everybody has the chance to grow up on an island,” Payet says.

He went back to France in 2005, spent two years at Nantes, then four at Saint-Etienne, but the disciplinary problems persisted. While he was at Saint-Etienne, he punched his team-mate Blaise Matuidi during a game in 2010. That did not stop him playing for France or Lille from signing him when they were the defending champions in Ligue 1 in 2011-12.

Payet’s was a wayward but gifted talent and he was dropped at one point last season by Marseille’s manager, Marcelo Bielsa. There was talk that he was being punished for slacking off in training. West Ham need a player who will turn 29 in March to be mature.

One theory is that his footballing upbringing in Réunion makes him more unpredictable than players who have been taught in academies in France. Payet looks thoughtful when that is put to him. “In Réunion it’s more physical,” he says. “It’s more difficult because of the sun. It’s in Africa and it’s maybe why we’re more technical.”

After two years at Lille, he joined Marseille and Bielsa’s manic coaching brought the best out of Payet last season. “I only spent one year with him but I learned a lot,” he says. “I feel I learned enough for the next 10 years.

“It’s true it takes a lot of concentration and focus to work with him, he does give a lot of detail. But even though it is hard work, once you’ve integrated those skills, it becomes easy on the pitch. It becomes natural.”

Now he is in England, Payet hopes to follow in the footsteps of players such as Eric Cantona, David Ginola and Thierry Henry. “All of them are inspirations,” he says.

“I cannot pretend I am as good as those players. I’m just starting, but who’s to say, one day I might be at their level.”