The British PM said he was "shocked" by the gun and bomb attacks, adding: "We will do whatever we can to help."David Cameron has offered "thoughts and prayers" to the French people after at least 127 people were killed in Paris.
The Foreign Office says it is "urgently investigating" whether any British nationals have been caught up in the shootings or hostage-taking.
There will be "strengthened policing at ports" and more police at public events in the coming days, UK police said.
Met Police Assistant Commissioner Mark Rowley, national policing lead for counter terrorism, called for "vigilance" from the public.
Downing Street said the prime minister would chair a meeting of the government's Cobra emergency committee in the wake of the attacks.
Many public places in Paris have been closed in the wake of the attacks.
Transport to the French capital from the UK has been affected, with delays and fewer people choosing to travel:
Eurostar passengers are being advised to arrive an hour early to St Pancras International due to expected delays.
British Airways warns of delays to Paris flights due to extra security checks.
Air France also says delays are expected following the "reinforcement" of border controls.
Easyjet says flights are operating as normal, but passengers are asked to check their flights on the Flight Tracker page and to allow extra time for security checks.
The airlines are offering a variety of options for passengers who do not wish to travel to Paris.
BBC News correspondent Richard Lister, reporting from outside St Pancras International, said a Eurostar train which would have been expected to hold 700 people left the terminal with just 200 on board.
The French national stadium, where France were playing Germany, was among the venues targeted by attackers on Friday.
Irish rock band U2 have cancelled a concert due to take place in the French capital on Saturday night.
A statement on the band's website said the decision was taken "as a result of the ongoing state of emergency across France" but organisers were "fully resolved to go ahead with this show at an appropriate time".
People were shot dead at bars and restaurants at five other sites in Paris. Eight attackers are reported to have been killed.
Gunmen reportedly killed 80 people and took dozens hostage at the Bataclan concert hall, where US rock group Eagles of Death Metal were playing. The siege ended when security forces stormed the building.
French President Francois Hollande said the attacks were "act of war" organised by Islamic State.
He has declared a state of emergency and indicated he would tighten border controls.
Mr Cameron, who had earlier appeared at a rally at Wembley Stadium with his Indian counterpart Narendra Modi, reacted to events in France via Twitter.
A Foreign Office statement said it was "very concerned" about the attacks, adding: "We are in close touch with the French authorities and are urgently investigating whether any British nationals are caught up in them."
It said people with concerns about British relatives or friends in Paris should call 0207 008 0000.
Foreign Secretary Philip Hammond tweeted that he had "conveyed my condolences" to his French counterpart Laurent Fabius, adding that the UK "stands with France".
The Prince of Wales is to send Mr Hollande a message of "profound sympathy and solidarity with the people of Paris", a Clarence House spokeswoman said.
Tweeting about the "deep tragedy", Archbishop of Canterbury Justin Welby said: "We weep with those affected, pray for deliverance and justice."
As news of the killings emerged, Scottish First Minister Nicola Sturgeon tweeted that it was "getting more horrific by the minute". She later added: "The thoughts and prayers of Scotland are with the people of France tonight. #solidaritywithparis."
Ask me one on one.