Just as François Hollande's cash-strapped government pulls the plug on a score of expensive French state arts projects launched by his rightwing predecessor, one exorbitant aluminium structure has bucked the trend.

Paris's futuristic new classical concert venue, the Philharmonie de Paris – a vast metal construction which promises to transform the northern Paris skyline – is on track to become one of the world's most expensive concert halls despite attempts by some politicians to block it because of its spiralling price tag.

State auditors have also expressed gripes, but the government has decided the building work is so far advanced that nothing can halt the cultural juggernaut. It is likely to open its doors, two years late, in 2015, after delays, suspension, rows and rocketing budgets – and after having more than doubled in cost to a staggering €387m (£316m).

The 2,400-seat concert hall will sit in the Parc de la Villette, on the north-east edge of Paris, near the city's peripheral ring road and the grey dual carriageways that lead to the rundown suburbs.

Its creators argue that it will not only end Paris's long-running shame about its lack of purpose-built classical music venues to match Berlin or London, but it will revolutionise attendances by attracting, young, "non-elitist" classical concert audiences.

The extravagant metal-encased building, likened to a stack of giant paving stones reflecting the city, is the latest Paris creation by the French "starchitect" Jean Nouvel, whose previous designs include the Institut du Monde Arabe and the controversial Quai Branly ethnographic museum.

He has described the Philharmonie as "the most prestigious project" of his career. The planned metal-clad roof is likened to a hill which visitors can climb. The 52m (170ft)-high aluminium slab at the top, which will have the concert listings projected on it, will be visible from the ring road so people sitting in traffic on the famously drab, grey motorway can see what's on.

But French state auditors have warned of the "exorbitant inflation in costs" of the project that is publicly funded by the state and the city of Paris. Another senate report complained of a "worrying drift" in the budget, asking whether the project really had to be so "grand" and did Paris really need it?

The green party in Paris angrily abstained from a vote to grant more city cash, warning of a "bottomless pit" for the public purse in a time of financial crisis. Paris city hall defended the project as "more than just a concert hall", calling it a daring and necessary bid to renew classical music audiences.

While several other cultural projects are to be shelved, including Nicolas Sarkozy's controversial pet project for a new national history museum, the Socialist Hollande might now end up having to borrow Sarkozy's own cultural catchphrase uttered in defence of the criticised exorbitant state funding of the Philharmonie: "Who can argue that in this time of crisis we don't need music?"

• This article was amended on 10 January 2013 because the original said Philharmonie de Paris is on track to become the world's most expensive concert hall. This has been corrected to say one of the world's most expensive concert halls.