Authorities in France have placed more than a third of the country under a red heat alert, cancelled some outdoor sports events and restricted alcohol consumption at the nationwide Fête de la Musique event amid a brutal heatwave forecast to push temperatures above 40C.

Level one or two heat alerts were issued on Sunday for about 53 million people, or 76% of the population. A record 35 of the country’s 96 mainland departments were put on danger-to-life red alert, with another 45 under an orange warning.

The national weather service, Météo-France, said: “Very high temperatures are setting in for the long term,” with a heatwave of “exceptional severity and duration” likely to break monthly and possibly all-time records.

It warned that temperatures could exceed 40C in many places on Sunday, with some areas facing rises to 42C or beyond from Monday. The national heat index, an average of day- and night-time highs at 30 weather stations nationwide, is also expected to hit its highest ever level, the forecasters added.

Sunday’s Fête de la Musique is a nationwide summer solstice celebration held every year that sees musicians take over the streets with free performances and revellers party into the night. This year’s festival is a particular source of heat-related health concerns, especially in Paris, Lyon and other major cities.

France’s culture minister, Catherine Pégard, urged “extreme vigilance” and said it should be up to local authorities to decide whether festivities should be cancelled or take place with suitable precautions. Most have opted for the latter.

Several towns have cancelled pre-7pm performances or moved them indoors. Many have introduced alcohol restrictions, with drinking banned on the street and in public spaces in areas on red alert and no alcohol on sale at municipally organised events.

In Paris, which is under a red warning, stronger drinks including high-alcohol beers, fortified wines and spirits have been banned along the banks of the Seine and the Canal St-Martin, to reduce the risk of people falling in. However, drinking at licensed bars and cafes and their terraces – where many gigs take place – is permitted.

Nearly 5,000 police have been deployed across the capital for the day and evening, as well as 2,500 emergency and health service workers. Paris city hall has also installed more than 1,300 free public water fountains, while more than 1,500 local shops have signed up for a scheme promising to fill personal water bottles without charge.

France’s prime minister, Sébastien Lecornu, convened a government heat crisis meeting on Saturday and planned another on Sunday, ordering ministers to urgently plan for better adapting France to further heatwaves in the future.

Scientists have said that as the Earth continues to warm, extreme heat events historically confined to high summer will become more frequent and more intense and last longer, as well as happening earlier and later in the year.

The French education minister, Édouard Geffray, said on Sunday that more than 800 schools across the country had already announced they would not open on Monday because of the extreme heat, while another 1,800 were rescheduling classes and end-of-year exams.

Jean Castex, the head of the SNCF state rail service, advised “more vulnerable passengers” to avoid taking the train and postpone journeys if possible, warning that air-conditioning systems and other rail infrastructure were being “heavily tested” by the conditions.

The heatwave is not confined to France. In Italy, authorities expanded heat warnings for Sunday from seven to eight cities in northern and central parts of the country, out of the 27 cities monitored nationally by the health ministry.

In Spain, the national weather agency, Aemet, has issued red warnings for northern regions. Temperatures between 40C and 42C are forecast in the major river valleys and inland areas such as Andalucia and Extremadura, rising to nearly 44C by Tuesday.

In the UK, the Met Office said baking heat could last until at least Thursday, sparking health alerts and concerns for vulnerable people. Forecasters have said there is “growing confidence” this week could break the record for the hottest UK June temperature of 35.6C, which was set in Southampton in 1976.