The mother of two young boys who were found dead in a car during a heatwave in France forgot about her children while she was shopping, it has been claimed. 

The brothers, aged just four and two, were found unresponsive by their mother on Monday afternoon in the French town of Carpentras in a car parked outside their grandmother's house. 

They suffered cardiac arrest as temperatures reached a sweltering 40C, and while services were called to the scene, resuscitation efforts were unsuccessful. 

Initial information released by the prosecutor's office suggested the children had 'allegedly locked themselves' inside the vehicle. 

However, it has now emerged that the boys' mother claimed to have 'forgotten her children' while shopping, French daily Le Parisien said, citing a police source. 

An investigation into manslaughter has been launched, according to the public prosecutor's office. 

The children's bodies have been transferred to the forensic institute in Nîmes for an autopsy, which will take place on Wednesday. 

France is being hit by a sweltering heatwave, with much of the western and central regions of the nation blasting past 40C on Monday. 

The hot temperatures continued into Tuesday, with highs of 43C. 

Harsh temperatures are expected to linger throughout Europe until at least Thursday, with conditions possibly intensifying as the week continues. 

The European heat dome comes after a May that saw several countries report record temperatures for that time of year. 

Weather bosses in France have put 49 of the 96 mainland departments on a red alert weather warning, up from 35 over the weekend.

Forecasters warned that scorching weather could end up being as serious as a 2003 heatwave that claimed the lives of nearly 15,000 people nationwide.

France's junior minister for ecology Mathieu Lefevre said this heatwave was 'particularly intense and particularly early'.

At Sunday's Fête de la Musique, which sees large crowds celebrate on the streets of most of France's cities, authorities banned the consumption of alcohol for fear of the risks drinking in high heat poses.

The Louvre also cancelled a free concert under its world-famous glass pyramid.

French citizens tried to cool down by visiting their local rivers and pools. But 13 tragically drowned over the weekend, authorities said.

The government's emergency response cell warned people not to try to cool off in unsupervised areas such as lakes and rivers.

Officials announced the closure of 845 schools on Monday, with another 1,800 set to let students leave earlier than normal.

Transport over the weekend and into Monday was affected in France. Jean Castex, the chief of state-owned rail operator SNCF, said high temperatures increased the risk to overhead powerlines and could even expand the tracks trains rely on.

As a result, SNCF cancelled 71 intercity trains Sunday through Monday on key routes, while deploying 3,500 staff to monitor the network. On top of this, 2,000 were sent to make emergency repairs.

Europe has suffered greatly from heat over the last few years. The World Health Organisation's Europe office said this month that over the last four years, more than 200,000 people across the continent died from heat-related causes.

The UN has warned that the weather over the next five years will likely see more shattered heat records.