Flight number BA0303 was held on the tarmac at Charles de Gaulle and surrounded by police and fire vehicles at around 8am UK time this morning.
British Airways said: “The safety and security of our customers and crew is always our top priority.
“Additional security checks are being carried out as a precaution.
“We would never operate a flight unless it is safe to do so.”
At around 11.10am, a British Airways spokeswoman confirmed the flight had taken off.
The airline did not state the nature of the alleged threat.
British traveller James Anderson, 20, tweeted a snap of the plane and security services.
He posted: “On British Airways flight BA0303, currently being held on tarmac at Paris due to security threat, surrounded by police and fire vehicles.”
He added: “Apparently an individual has made a direct threat to this aircraft.
“We will all be led off the aircraft and baggage searched in due course.”
He then posted: “Everybody’s been individually searched by armed officers and given all clear.
“Now hold luggage being searched by dogs.”
Mr Anderson later tweeted: “Pilot: ‘Aircraft has been deemed absolutely safe. Authorities are satisfied with the search. We will continue on to London Heathrow’.”
He added: “Our pilot was an absolute credit to @British_Airways. Extremely calm and composed, handled the situation wonderfully.”
The security alert comes amid heightened tensions in the UK in the wake of the failed bomb plot on a District Line train at Parsons Green on Friday.
Intelligence chiefs raised the threat level to “critical” meaning that a second attack could be imminent.
France has been one of the countries hardest hit by terror attacks in recent years, with 130 killed in the Paris attacks in November 2015, and 84 killed in the Nice attacks in July last year.
There have been a number of smaller attacks, while the doomed EgyptAir flight MS804 which crashed into the Mediterranean in May 2016, possibly due to an explosion, also took off from Charles de Gaulle.