France’s national weather agency Meteo France said the heat wave beginning on Monday is expected to last all week with temperatures of up to 40C (104F) across the country.
The peak is expected on Thursday.
In Paris, charity organisations are patrolling the streets to provide water to homeless people and local authorities have organised air-conditioned places where they can seek shelter.
Meteorologists say the heat wave is caused by hot winds coming from the Sahara Desert.
The alert system was introduced in France following the summer of 2003, which saw an estimated 15,000 heat-related deaths, many of them older people left in city apartments and retirement homes that were not air-conditioned.
French health minister Agnes Buzyn said on Monday that “everything is ready, in retirement homes, in hospitals, in transports.”
“Yet when people are fragile, even when everything is organised, there’s always a higher mortality rate,” she warned.
Organisers at the Women’s World Cup, which is being hosted by France, could be faced with implementing Fifa heat precautions, since knockout games are being played every day this week except Wednesday and Sunday.
In Germany, temperatures above 40C are possible in some places on Wednesday, topping the country’s previous June record of 38.2C (nearly 100.8F) set in Frankfurt in 1947.
Rescue services have urged people to look out for young children, the elderly and those with compromised immune systems who are at particular risk in high temperatures.
Parts of northeastern Germany are also at high risk for forest fires.
Authorities in the eastern state of Brandenburg, which circles Berlin, say the risk of forest fires is at the highest level in the coming days.
In Ireland, temperatures could reach 28C by the end of the week, with “exceptionally warm” weather being forecast for Friday.
“It’s going to be a warm start to the week and by the looks of it, it’s going to be even warmer later in the week,” said a Met Éireann forecaster.
“The weather is not completely settled and we expect to see some thunderstorms but they are going to be isolated.
“They are not going to be persistent.”
“It won’t be wall-to-wall sunshine initially but there will be strong spells of it.
“And later in the week it will be way warmer than usual,” the spokesperson added.