Italian sovereignty should be jealously guarded, said MPs from the League, the Right-wing party led by Matteo Salvini, who was deputy prime minister and interior minister until last summer.
“The unilateral annexation by France of a highly symbolic piece of Italy is an affront,” MPs said in a statement.
Soaring 15,781 ft (4,810m) above sea level, Mont Blanc straddles the border between the two countries, with the French town of Chamonix on one side and the Italian ski resort of Courmayeur on the other.
The ordnance about environmental protection, which includes safeguards for the mountain’s plants and wildlife, was issued earlier this month by the French.
It pertains to large tracts of the French side of the border but also strays into Italian territory – a glacier known in Italian as the Ghiacciaio del Gigante and in French as the Glacier du Géant, as well as a mountain refuge, the Rifugio Torino.
The regulations were issued jointly by the French towns of Chamonix-Mont-Blanc, Houches and Saint-Gervais-les-Bains.
Many on the French side of the frontier believe the row has more to do with Italian politics than a genuine territorial issue.
Éric Fournier, the mayor of Chamonix, told The Telegraph the Italian government appeared to have misunderstood the French ordinance, which he said had “very clearly” applied only to the French side and only for a few days.
“We banned paragliding during an anti-cyclone that created a heatwave which made conditions dangerous for paragliders. This is either a misunderstanding or a nationalist upsurge; either a mistaken interpretation or a deliberate intention to make a territorial claim.”
Jean-Marc Peillex, the mayor of Saint-Gervais-les-Bains, said the priority was to protect Mont Blanc from overtourism and environmental damage.
“This is a political debate disconnected from reality on the ground,” he told The Telegraph. “When there’s an accident, the emergency services from both Italy and France intervene. No one worries about whether they may have crossed the border because the important thing is to save lives.”
Mr Peillex, whose municipality includes an enclave surrounded by Italian territory, added: “Italy has sometimes objected to the border but it has long been accepted by local people. This is a story from a bygone era.”
Italy and France have been battling over Mont Blanc ever since the 1860s, when Italy was unified and established as a modern nation state.
The two sides of the mountain range still have close cultural and linguistic ties – the Italian region of Val d’Aosta, which includes Courmayeur, has French as its second language and retains a distinctly Francophone feel.
On social media, some Italians were indignant over the purported French provocation. “Let’s dispatch a few Alpini (the Italian army’s mountain warfare troops) to send a message,” said one Twitter user.
“We’ve lost the respect of other countries, no wonder they treat us like this,” wrote another.