British passports are now made by De La Rue, which despite its French name is a British company that prints them in northern England. The company's CEO said it lost the tender for the new version after being undercut on price.
Franco-Dutch company Gemalto won the contract, the Sun newspaper said.
"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," De La Rue CEO Martin Sutherland told BBC radio.
I'd like to invite Theresa May or (interior minister) Amber Rudd to come to my factory and explain to my dedicated workforce why they think this is a sensible decision to offshore the manufacture of a British icon."
"Sacre Bleu!" headlined the pro-Brexit Daily Mail tabloid.
When May announced the switch back to blue passports in December, she said on Twitter: "The UK passport is an expression of our independence and sovereignty - symbolising our citizenship of a proud, great nation. That's why we have announced that the iconic #bluepassport will return after we leave the European Union in 2019."
The European Union does not require any particular colour of passport but recommends member states adopt burgundy. Croatia, which joined the European Union in 2013, retained its blue passport with no plans to change its colour scheme.
De La Rue's contract, which ends in July 2019, is worth 400 million pounds ($566 million). Its shares fell 5 percent in early trading.
Britain's interior ministry defended the decision.
"The preferred bidder has been selected following a rigorous, fair and open competition," it said in a statement.