The high-speed rail project between Lyon and Turin is strongly opposed by the anti-establishment Five Star Movement (M5S), which rules at a national level with the far-right League.
But the region of Piedmont, where the train line would end, is now under the control of a right-wing coalition of parties, after the M5S suffered defeat in the recent regional elections.
The League, the small far-right Brothers of Italy (FdI), and Silvio Berlusconi’s centre-right Forza Italia (FI) won nearly 50 per cent of votes in the region, compared to 36 per cent taken by a left-wing coalition.
The M5S only garnered 13 per cent of votes in the Piedmont.
The right now holds all the main regions in the country’s wealthy north, from Liguria to Lombardy, Piedmont and Veneto.
The M5S had been campaigning actively to end construction of the high-speed rail link, holding protests in Piedmont against a project it argues is bad for the environment and a waste of public money.
The €8.6-billion tunnel through the Alps, which has already been partially built, would cut travel time between Milan and Paris from almost seven hours to just over four.
Supporters of the rail link, launched nearly 20 years ago and officially scheduled to be finished in 2025, claim it would lead to a reduction of 1 million trucks and around 3 million tonnes of greenhouse gas emissions every year.
The right-wing coalition is in favour of the project.
Following poor results in the recent elections, M5S leader Luigi Di Maio appeared to soften his stance on the rail link on Monday, saying the project was now in the hands of the prime minister.
Preliminary tenders to continue work on the rail link have been launched, but Italy and France had six months from March to revisit the project before making a definitive decision.
France supports the rail link, as does the European Union, which has already provided hundreds of millions of euros in funding to the project.