Red heat alerts have been issued in France, Spain and other nations across western and central Europe as heatwave conditions are forecast to intensify in the coming days with highs of more than 40C.

More than half of France's regions are currently under the harshest weather warning, with hundreds of schools ordered to close and highs of 42 °C hitting Bordeaux on Monday, forecaster Météo-France said.

Two children aged two and four have been found dead in their family car in the town of Carpentras in southern France, in an accident being linked to the weather.

Similar red warnings have been issued by the authorities in Germany, Italy, Switzerland and Luxembourg.

The rising temperatures are being driven by hot air moving north from the Sahara desert, which is in turn trapping hot air over the affected areas, with forecasters suggesting the conditions could result in one of the longest heatwaves in recent years.

Scientists have said that recurring heatwaves are a marker of global warming, with Météo-France noting that of the 51 heatwaves recorded in France since 1947, 34 have taken place since 2000 and 26 since 2011.

Elsewhere, the conditions have seen:

• Spain's state weather service Aemet warns of "extremely high" temperatures for the season until Wednesday, between five and 10 degrees above what is typical, with some areas set to reach 44C.A red alert has been issued for the Basque Country, with highs in San Sebastian forecast to rise to 40 °C, almost double its average for this time of year
• Italy issued red alerts for 12 cities, including Milan, Turin, Venice, Bologna, Florence and Rome, after several days of temperatures above 35 °C
• Five people die in fatal swimming accidents over the weekend in Germany, where temperatures have already reached as high as 38 °C
• The UK's Met Office issued a rare red heat warning for Wednesday and Thursday for parts of England and Wales, amid forecasts suggesting temperatures could reach 38C in some areas
• Firefighters battle a wildfire near Akraifnio, in central Greece, that has forced the temporary closure of a major motorway following hot, dry weather and strong winds
• The IRM meteorological institute in Belgium is forecasting record temperatures in the coming week. Meanwhile, the country's train operator announced some peak-hour trains would be cancelled on Monday and Tuesday due to the heat

Temperatures are expected to peak in many parts of the continent on Wednesday, with 41C forecast for Paris.

In the capital on Monday, several train lines also reduced services. France's national railway operator SNCF urged "vulnerable" people to avoid or postpone train travel this week.

Some 845 schools in France were shut, while a further 1,800 are allowing pupils to finish classes early, the education ministry said. But more than a million high school students were taking their oral final exams for the baccalaureate amid the heat.

A red heat alert is the highest of four warnings issued by Météo-France and advises people to exercise extreme caution in potentially life-threatening conditions.

Dozens of other regions in France are under an orange alert - the second-highest warning - with an estimated 63 million people across the country affected.

The full circumstances of the deaths of the children found in their family car in the south of France are not yet clear, but they had been returning from a shopping trip with their mother and reportedly found themselves stuck inside the family car with the windows shut, amid temperatures of 39 °C.

Ambulance workers tried unsuccessfully to resuscitate the pair.

The local state prosecutor said the precise cause of death had yet to be determined, but "it is probably linked to the heatwave".

Meanwhile, the French government has urged people not to try to cool off in unsupervised areas such as lakes and rivers, after 13 drowning deaths over the weekend.

In the south-west Gironde region, local authorities on Sunday said three people - aged between 80 and 95 years - had died, partly due to the intense heat.

The conditions in France follow a weekend in which the mercury hit 40C, prompting an alcohol ban at the annual Fête de la Musique, a national festival that draws large crowds onto the streets of most cities.

The ban applied to all events organised by the French state and its agencies, and aimed "to preserve emergency and healthcare services and allow medical staff to focus on caring for the most vulnerable", the government said.

While the hottest temperatures are expected along the western coast, highs are expected to range from 36C to 40C across much of the rest of the country, Météo-France said.

The forecaster warned that the heatwave will be "widespread, long-lasting and intense" - with temperatures not expected to drop until the end of the week.