Passengers on board Friday’s flight LS1204 from Malaga to Birmingham say the aircraft was tracked by a military plane for up to 15 minutes.
Sarah Hatfield, from Quarry Bank near Dudley, was travelling with her husband Ian and their 13-year-old daughter Emily.
She said: “Someone spotted the French jet and told the cabin crew, who I presume told the Jet2 pilots. The air stewardess then announced there was nothing to worry about.
“Ian was terrified and it didn’t help that loads of other passengers came by us to look out at it.
“It was so close I could read the writing on its tail fin. The feeling on board was a mixture of excitement at seeing the fighter so close up and terror as to if we were about to get shot down.”
A spokesperson for Jet2 said: “We are awaiting clarification from the French air traffic authorities, as to why a military aircraft was apparently tracking our aircraft”.