Ten minutes to kick-off at Monaco's match against Lorient last Sunday, the yachts in the Cap-d'Ail marina just visible from inside the Stade Louis II, came confirmation that the striker all Europe relishes watching would start for Monaco. "Numero neuf," roared the stadium announcer, of the Colombian for whom Monaco paid Atlético Madrid that startling €60m this summer: "RA-DA-MEL FALCAO!"

To say the crowd went wild would be exaggerating just a little. Assembled to watch Falcao, live on the Côte d'Azur, with João Moutinho, midfield rock signed for £22m from Porto along with James Rodríguez, who cost £40m; fearsome French international Geoffrey Kondogbia, who cost £18m from Sevilla; and languid veterans Ricardo Carvalho and Eric Abidal, were 8,500 people. Three stands in the old stadium were patchily occupied by a leisurely crowd. The curved "tribune" stand beneath the famous nine arches was glaringly empty.

This is the new Monaco, £146m spent on summer signings backed by the Russian billionaire Dmitry Rybolovlev, playing at the top of Ligue 1 to crowds more suited to League One. On Sunday Monaco play Qatar-owned Paris Saint-Germain, a contest of overseas mega-wealth that seems blaringly at odds with French football's traditional rhythms.

They say that in Monaco – the tiny, plush principality stubbornly independent of France, ruled for centuries by the Grimaldi royal family, where Europe's super rich come to live free of tax – they have always struggled for a football crowd. This was so when Glenn Hoddle signed for Arsène Wenger in 1987, through the 1990s when Wenger and a cadre of French greats, including Thierry Henry, Emmanuel Petit and Lilian Thuram were making their reputations, and as recently as 2004, when coach Didier Deschamps led Les Rouge et Blanc to the Champions League final, where they lost 3-0 to José Mourinho's Porto. Yet to see this team of stars, amassed with so much money and the hefty involvement of the agent Jorge Mendes, stroll to a 1-0 victory amid such emptiness came as a shock.

Claudio Ranieri, the Chelsea manager until Roman Abramovich hired Mourinho after that 2004 Champions League victory, and latterly coach at Internazionale, Roma and Juventus, has been recruited by Monaco, at 61, as the football man of authority, to bring order and basic values to an extraordinary situation. Asked about the half-full stadium, Ranieri said Falcao and his team-mates must just concentrate on the game:

"Everything is not the same here; in Monaco there are not a lot of fans because it is a little city," Ranieri said. "For this reason we chose the right players, who have the right mentality. They are very professional players."

There have been reports that Falcao, who scored the match-winning penalty with faintly dismissive ease, is unhappy already. After the match, smiling, he declined to talk to the press. Ranieri, though, waved away the suggestion. "No, Falcao is very happy, he is a professional, 100%. He has his daughter here. He is living here very well."

Around the club, they smiled that this crowd was actually encouraging; more than double those of two years ago when, with Deschamps and the greats long gone, Monaco fell to the bottom of Ligue 2. The club that bears the principality's flag and royal crown on its badge was always owned by the Grimaldis, who built the stadium and provided financial support to a sporting emblem of Monaco. But with a government now under Prince Albert, who acceded to the throne in 2005, keen to present itself as financially responsible rather than overseeing, in Somerset Maugham's unbeatable phrase, "a sunny place for shady people", state funds were not made available in the quantities required for modern top-flight football.

Rybolovlev, 46, clambered to the ranks of Russia's post-communism super-rich by acquiring a major stake in a potassium producer, Uralkali, in the mid-1990s. He held on to it through 11 months in prison in 1996-1997, when he was charged with ordering a contract killing, in the free-for-all that followed communism's collapse. He was acquitted, then continued to build up Uralkali, ultimately selling a 53% stake for a reported $5.3bn. By then, Rybolovlev was conducting much of his business via Cyprus, and lived in Switzerland, until he arrived in Monaco in 2010.

He was pursued by his former wife, Elena, who is determined to claim a divorce settlement proportionate to Dmitry's massive wealth, arguing that she always stood by him, from when they met as students in their home town of Perm.

Elena has obtained a court order in Switzerland freezing Dmitry's assets there but has not succeeded in applying it to trusts set up by Dmitry in the names of the couple's children, Ekaterina and Anna, for, according to Dmitry's representative Sergey Chernitsyn, "succession planning". Chernitsyn stresses that Rybolovlev did not buy the 66% majority stake in Monaco in 2011, a landmark deal with Prince Albert, taking the club out of royal family majority ownership for the first time. The stake, Chernitsyn pointed out, has been bought by "the trust acting on behalf of Ekaterina Rybolovlev", Dmitry and Elena's 24-year-old daughter. The trust is the investor, Chernitsyn says, while Dmitry is the club president.

Dmitry makes public statements rarely but he did tell L'Equipe this summer: "I have done everything to secure the future of our two daughters and I am only defending their interests."

In crisis before Rybolovlev arrived, Monaco made a £2.6m profit on player trading in 2011-12, as good players left after relegation, including Park Chu-young, whom Arsenal bought for £5.7m. The new regime stabilised the club in Ligue 2, Ranieri was recruited in 2012 by the then sporting director Tor-Kristian Karlsen, amid a flurry of signings, and the Italian won promotion in his first season. Then Monaco unrolled this summer's lavish signings, with Falcao the most lavish of all.

Mendes, the Portuguese agent who acts for Mourinho and a roster of Portugal internationals, has been centrally involved in delivering the players. Mendes acts for Falcao, Rodríguez, Moutinho and Carvalho, agreeing their moves for stellar salaries – Falcao is said to be paid €1m a month.

All those players have in their careers been subject to "third-party ownership" – investment companies buying the right to a proportion of a future transfer fee – which is outlawed in the UK and in France. Porto bought back 35% of Rodriguez's economic rights from a Luxembourg-based company, Gol Football, in February, before selling him to Monaco in July. Porto sold 37.5% of Moutinho's economic rights for €4.125m after he signed from Sporting Lisbon in 2010; bought the right-back in two chunks, in August 2011 and January this year for a total of €7.3m, then sold the 27-year-old to Monaco for £22m.

Mendes's agency, Gestifute, has denied reports that he owned a proportion of Falcao's rights via a company, Doyen Sports, based in Malta, another low-tax European country. José Díaz, a spokesman for Doyen, told the Guardian the company was paid 33% of the Falcao transfer – €20m – because Doyen helped to finance Falcao's original signing by Atlético Madrid.

Díaz, who said Mendes has no involvement with Doyen, said the company was also paid from Monaco's fee for Kondogbia, "because we financed [Kondogbia's] signing from Lens to Sevilla".

On the Friday before the Lorient match, under a brilliant sky at the La Turbie training ground, hewn out of the cliffs above Monaco, Ranieri played down the sense of abnormality. He was glad, he said, to have been appointed at the start of a project, his job as coach to mould the new arrivals into a coherent team. "I am an ambitious man; I want to build, to win, to explain my philosophy to my players," he said. "The money is important, but it is not so important. The organisation is important, the feeling between the players and the coach, to think about how you can improve."

Rybolovlev does have a long-term strategy, Ranieri added, a mapped out plan that involves signing young players alongside the ageing stars, and building football strength over time. "Of course, the money helps to win because with the money you can buy the right good players and champions, but money isn't everything."

Competing clubs in the Ligue de Football Professionel have not, though, viewed Monaco's sudden riches so philosophically. Under its treaty with France in 1963, Monaco agreed its French residents would pay tax at French rates, but those from overseas, the majority now including millionaire footballers, would pay no tax. As France's top tax rate is 49%, the league has calculated Monaco are saving €50m a year on the salaries of the overseas stars in PAYE that the other clubs have to pay.

In March the league acted, ruling that from next season all its clubs must be registered in France for tax purposes, a move clearly aimed at Monaco. A meeting in Rybolovlev's Monaco penthouse with the French football federation president, Noël Le Graët, did not go well, and Rybolovlev took the league to court, where the case remains unresolved.

Nobody at Monaco would discuss the tax issue, given its sensitivities, but the league remains insistent. Its president, Frédéric Thiriez, told Le Parisien last week: "Everybody is very happy that Monaco have returned to Ligue 1. But I am sorry, there is a problem of fairness. I have calculated the differential at €50m, a precise calculation, €50m is the budget of Montpellier, this is not a negligible advantage. We are not hounding them; we have given them a year to conform."

The other looming cloud on Monaco's sunny new future is Uefa's financial fair play rule, which aims to prompt clubs to live within their means, just as Ekaterina Rybolovlev's trust has sprung Monaco clear of theirs. The club's accounts for the 2011-12 financial year show they just about broke even, with player sales balancing the books, but that was before the £146m spent on players and eruption of the wage bill this summer. Uefa's rules allow total losses of €45m over the 2011-12 and 2012-13 financial years, with sanctions for noncompliance extending most punitively to exclusion from the Champions League, Rybolovlev's absolute target. Monaco's sudden extravagance could yet prove tricky for Uefa, which hosts its glitzy Champions League draw every year at the Grimaldi Forum, on the Mediterranean seafront – in Monaco.

Konstantin Zyryanov, the chief executive recruited by Rybolovlev from the Commercial Bank in Moscow, smiled when asked how the gap between the mega-cost of the players and income from a crowd of 8,500 can be bridged. "It isn't easy," he said. "We are working hard to attract people; already this season we have made more money than in the whole of last year. We have a lot to do."

The commercial director, Bruce Bundrant, an American, came to Monaco after five years as head of sponsorships and international tours at Liverpool, first under the ownership of Tom Hicks and George Gillett, then John Henry's Fenway Sports Group. He said Monaco is a similar prospect to PSG where "new ambitious owners have invested a lot in the team and the commercial side must match up", but Monaco cannot earn from sponsorships in the owners' home country, as PSG have done. He is grappling with Monaco's contradictions as a club: a name that evokes classy football and prestige, yet, unlike Liverpool, in a place of sun, yachts and a small population mostly of tax exiles, with pastimes other than football.

"But people in the club are confident they can make a sustainable business here," Bundrant said. "We are really using the attributes of Monaco – luxury, elegance; what a special place this is. Sponsors can see this is a sexy team, cool atmosphere in the principality, we're aiming to have the best hospitality, to match the superstars on the pitch."

"This is," he said, in the main stand of the half-full Stade Louis II, "one of the sexiest projects in European football."