They are accused of involvement in the abduction last year of Amir Boukhors, 41, a critic of Algeria's government with a large audience on social media, who was reportedly granted asylum in France in 2023.
Barrot urged Algeria to "abandon" the expulsions and said France was ready to "respond immediately" if they went ahead.
"I am asking Algerian authorities to abandon these expulsion measures... if the decision to send back our officials is maintained, we will have no other choice but to respond immediately,' he said.
He claimed that the expulsions were a response to the indictment of three Algerian nationals in Paris, including the consular official, on charges including abduction, arbitrary detention and illegal confinement and participating in a terrorist organization.
Algeria's foreign ministry said it had summoned French ambassador Stephane Romatet in response to "express its strong protest" and called for the official's immediate release, according to the official Algerian news agency.
Boukhors, also known as Amir DZ who has lived in France since 2016, was abducted in April 2024 in the southern suburbs of Paris and released the following day, according to his lawyer Eric Plouvier.
Plouvier told the media that Boukhors had been "the subject of two serious attacks, one in 2022 and another on the evening of April 29 2024".
French media reported that he was forced into a car with a flashing light by "fake police officers", then released the next day without explanation.
Algeria has issued nine international arrest warrants against him, accusing him of fraud and links to terrorist organizations. He denies the allegations. In 2022, the French courts refused his extradition.
The case is the latest in a growing number of incidents to have exacerbated a rift between France and Algeria. They include the arrest and imprisonment in Algeria of French-Algerian author Boualem Sansal, who was accused of undermining Algeria's territorial integrity.
Algeria recalled its ambassador from Paris last year after France backed Morocco's claim to the disputed territory of Western Sahara. The 12 French officials asked to leave on Monday include some members of the French interior ministry.
It added that the individual "was arrested in public and then taken into custody without notification through the diplomatic channels."
The ministry claimed the move was "not a coincidence as it happens in a very specific context with the aim of stymying the process of relaunching bilateral relations".
Tentative steps have been made to repair relations between the two nations with a phone call between French President Emmanuel Macron and President Abdelmadjid Tebboun taking place in March.
"The two presidents had a long, frank and friendly exchange on the state of bilateral relations and the tensions that have built up in recent months," a joint statement read.
Following an official visit to Algeria on 6 April where he met with Tebboun, Barrot said he hoped for a "new phase" in relations.
IGIHE
