France has declared three days of national mourning after the attack in Nice.
The truck ploughed through crowds celebrating Bastille Day last night, driving for more than a mile before the gunman got out and sprayed the crowd with bullets.
The attacker - a 31-year-old Tunisian man known to police - was shot dead at the scene by armed French police. The attack, on France's national holiday, followed attacks in November in Paris that killed 130. "France was struck on the day of its national holiday, July 14, the symbol of liberty", Hollande said early Friday, denouncing "this monstrosity" - a truck bearing down on citizens "with the intention of killing, smashing and massacring...an absolute violence".
US President Barack Obama condemned "what appears to be a horrific terrorist attack", although no group had yet claimed responsibility.
Interior Minister Bernard Cazeneuve told reporters on the scene that the death toll stood at 80, with scores injured including 18 in "critical condition".
Security already had been reinforced at the Tour this year, with France in a state of emergency since the Paris attacks.
Bauke Mollema, who was involved in a crash with Froome inside the last kilometre of Thursday's Stage 12 at Mont Ventoux when a TV motorbike was forced to stop on the road because of fans congestion, said his "thoughts are with the people in Nice".
"We saw people hit and bits of debris flying around".
At the same time, in a move to promote the city as a go-to spot, the "Destination Paris" campaign was kicked off by French Minister of Foreign Affairs and International Development Jean-Marc Ayrault, Paris Mayor Anne Hidalgo and Valérie Pécresse, president of the Paris region council.
US Secretary of State John Kerry has told his Russian counterpart in Moscow that the attack in the French city of Nice showed the need to speed up worldwide efforts to tackle terrorism, especially in Syria. I will just sit at home and be haunted by this.
Mrs May said she was "aware of the reports there has been a Briton involved".
Nadr said he saw the driver pull out a gun and start shooting at police.
The Promenade des Anglais was sealed off, crawling with police and ambulances as authorities from the local Alpes-Maritimes prefecture urged residents to stay indoors.