The plan was opposed by environmental groups that set up camp at the proposed site in Notre-Dames-des-Landes, BBC reported on Wednesday.
But local politicians reacted angrily to the decision, suggesting it would have bad economic consequences.
The proposal for an air hub in the region has been the subject of fierce debate for nearly half a century.
Prime Minister Edouard Philippe said it was impossible to continue with the plans given the "climate of bitter opposition between two sides of the population that are nearly equal in size".
He also vowed to evict the environmental activists who have been camping at the 1,600-hectare (3,953-acre) rural site for almost a decade.
"We will put a stop to the no-go zone which has flourished in this area for nearly 10 years," Philippe said.
It is not yet clear whether the campaigners will leave peacefully. The first attempt to clear the site in 2012 ended in clashes, forcing the government into a retreat.
This has been one of the biggest planning fiascos of modern times.
It had the backing of successive regional and national governments, and went through an exhaustive process of approval. Legal appeals were rejected, the farm land was appropriated, and a multimillion-euro contract was signed to build it.
But environmentalists have always opposed the airport. For some years now the site has been occupied by hundreds of activists, who illegally built makeshift homes there and vowed to resist any attempt to remove them.
The threat of serious violence has stopped every previous effort to go ahead with construction, and now the government of President Emmanuel Macron has decided the best option is simply to abandon the airport completely.
President Macron, who took office in May, had promised a quick decision after years of debate over the proposal.
It had passed every stage of the planning process and was backed in a referendum.
Local officials say the government has turned its back on the democratic process and given in to the threat of violence from protesters.
The head of the local government, Philippe Grosvalet, accused President Macron of ignoring the result of the referendum.
"He's trampled on our local authorities and on the spirit of decentralisation," he said.
The cost of the airport was estimated to be $710 million.
But reports say the French group Vinci, which had been awarded the contract to build the airport, could be in line for a compensation payout of 350 million euros.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
