Chief executive Martin Sutherland today called for Mrs May to explain why the government thinks the move is "sensible." The plans sparked immediate anger among Leave supporters in the UK.
Passport firm De La Rue, which manufactures the UK’s current burgundy design, is expected to appeal the decision, which would see it lose out on a £490m contract to make the new ones.
Gemalto, which is listed on the French and Dutch stock exchanges and has a French chief executive, is believed to have undercut British and other rivals by £50million to win the contract.
Mr Sutherland confirmed his company would not be producing the new style of passport as he challenged the Prime Minister to explain the decision this morning.
Speaking on BBC Radio 4’s Today programme, Mr Sutherland called for an explanation on why the Government has decided to give the contract to a non-British manufacturer.
The Home Office last night said no final decision had been made. But Mr Sutherland refuted this, saying the printing job had been awarded to Gemalto.
He told the show: “I'm going to have to go and face those workers, look them in the whites of the eyes and try and explain to them why the British government thinks it's a sensible decision to buy French passports not British passports.”
A spokeswoman for the Home Office said: "We do not require passports to be manufactured in the UK.”
She added: "A proportion of blank passport books are currently manufactured overseas, and there are no security or operational reasons why this would not continue."
De La Rue had issued a profit warning on Tuesday, telling investors its profits for the coming year are likely to be “at the lower end of the current consensus range”.
Mrs May announced the return of the iconic dark blue passports, which are described by some Brexiteers as a powerful symbol of Britain’s restored sovereignty, in December.
It came as Brexiteers across the UK voiced fury at the plans.
Tory MP Sir Bill Cash, chairman of the Commons European Scrutiny Committee, branded such a move "completely wrong and unnecessary".
Former cabinet minister Priti Patel said: "To be putting the job in the hands of the French is simply astonishing. It is a national humiliation."
The head of pro-Europe campaign group Best For Britain, Eloise Todd, said: "The new the pro-Brexit blue passports were supposed to be a statement of intent and now we find out they are to be made by the French or the Dutch. The irony is unreal.
"I guess the Brexit Blue is now classed as French Navy."