Natasha Ednan-Laperouse, 15, collapsed while on board a British Airways flight from Heathrow to Nice on 17 July last year.
The inquest was told that before boarding the plane, the teenager had eaten an artichoke, olive and tapenade baguette bought from the main Pret a Manger shop in Terminal 5 at Heathrow Airport.
She looked desperately at her businessman father to save her life after two epipens were administered on board a flight to Nice, yet she still could not breathe.
She said: “Daddy, help me! I can’t breathe” before falling unconscious, the inquest heard.
She was declared dead hours later at a hospital in Nice.
The inquest heard evidence from the Pret store manager on the day, its head of food safety and compliance, as well as BA cabin crew and the pilot from the flight.
The five-day hearing, which began today, is expected to look at laws on product labelling and whether regulation needs to be tightened to prevent another incident.
Natasha’s father, Nadim Ednan-Laperouse, founder of the company Wow Toys, said: “As a family now of three, my wife, son and I are still trying to adjust to life without our beloved girl.
“It’s a daily battle and the pain is indescribable. Everything we say and do is a reminder that she isn’t with us; her empty bedroom, school uniform hanging in her wardrobe, her holiday bag packed for her holiday in Nice has never been unpacked. We can’t bear to.”
It is believed sesame was baked into the baguette eaten by the teenager, rather than in seeds on its crust.
Sesame is one of 14 allergens that EU law stipulates must be listed in pre-packaged foods.
However, outlets that prepare food on their premises, such as Pret, are not required to individually label their food products with such advice.
The distinction is intended to help small, independent food providers who would struggle to provide such packaging.
Pret a Manger confirmed that its products were not individually labelled with allergen or ingredient information. It pointed to signs on shelves and at tills informing customers that they should speak to a manager, who is trained to provide allergen advice.
A spokesperson for Pret said: “We were deeply saddened to hear about Natasha’s tragic death, and our heartfelt thoughts are with her family and friends.
“We take food allergies and how allergen information is provided to our customers extremely seriously. We will continue to do all that we can to assist the coroner’s inquest.”
This story also featured on our sister site inews.