The aircraft were launched from RAF Coningsby on Monday night to identify an unresponsive civilian aircraft, the Ministry of Defence said.
People reported hearing what sounded like two loud explosions which were later confirmed to have been sonic booms.
Air France confirmed that the unresponsive plane had been one of their aircraft but it later landed safely guided by the Typhoon jets.
An RAF spokesman said: “Quick reaction alert Typhoon aircraft were launched from RAF Coningsby to identify an unresponsive civilian aircraft. Communications were re-established and the aircraft has been safely landed.”
Air France tweeted from its official UK Twitter account that a radio communication problem caused the jets to scramble.
The message over two tweets said: “Air France confirms that due to a radio communication problem AF 1558 had to be accompanied by two British fighter aircrafts according to the procedure.
“The aircraft landed in Newcastle at 22.20 (LT). Safety of clients & crew is an absolute priority.”
North Yorkshire Police earlier tweeted to reassure people there was no danger, later writing: “Confirmation from RAF that loud bangs heard across the county were sonic booms from RAF Typhoon jets. No cause for concern.”
One woman wrote: “house shook & whole street was out, car & house alarms gone off. Apparently was a sonic boom.”
Another said: “Those vibrations shook my house and scared me to death. #QRATYPHOON had me out of my bed.”
Last month, two bangs heard around Northampton and Brackley were caused by Typhoon jets which had been scrambled from an RAF base in Lincolnshire to identify an unresponsive aircraft.