France has banned alcohol at some events at a massive national music festival on Sunday as a heatwave pushes temperatures towards record levels.

Annual Fête de la Musique celebrations draw millions to the streets across France. But with a third of the country covered by the most serious heatwave warnings, the government has banned alcohol consumption in public places under the red alerts.

"For all events organised by the state and its agencies, instructions have been given not to offer alcohol," the office of Prime Minister Sébastien Lecornu said.

Temperatures of 39-40C (102-104F) are expected from the southwest through the Paris region into Burgundy on Sunday, with some areas possibly reaching 41C.

Temperatures have been forecast to peak on Monday, and authorities have warned they could match historic highs.

The government has called for limits on alcohol consumption "to preserve emergency and healthcare services and allow medical staff to focus on caring for the most vulnerable".

The heatwave has been going for days and has disrupted the country, forcing the cancellation of dozens of trains and the suspension of classes.

France's weather service Météo-France said it was "uncertain" how long the heatwave, which has been estimated to affect about three quarters of the population, would last.

To help Parisians and tourists cope with the heat, authorities are keeping parks and gardens in the French capital open through the night.

Fête de la Musique has been going for more than 40 years, and is always held on the summer solstice.

Last year, about two million people attended events in Paris.