Italy limited work outdoors, France shut schools and Turkey battled wildfires on Tuesday in a European heatwave that meteorologists said was "exceptional" for striking so early this year.

French authorities imposed precautions nationwide in anticipation of peak temperatures on Tuesday, with some areas bracing for highs of 41C in a heatwave that has gripped all of Europe.

More than a thousand schools were closed in France on Tuesday and the top floor of the Eiffel Tower was shut to tourists as a severe heatwave continued to grip Europe, triggering health alerts across the region.

Punishing temperatures were forecast to reach 40 degrees Celsius (104 degrees Fahrenheit) in Paris and to stay unusually high in Belgium and the Netherlands. In contrast, temperatures were falling in Portugal, where no red heat warnings were issued.

Schools were partially shut in France, iconic monuments closed to tourists, and cities across Europe put on high alert as a record-breaking early summer heat wave spread across the continent Tuesday.