The Afghans, including around 70 interpreters, and their families will be able to gain a visa if it is determined their lives would be in danger if they stayed in Afghanistan, and could integrate into French society.
People who worked at French military bases as chefs, cleaners, handymen and in other capacities are also eligible to apply.
The Interior Ministry told the news agency AFP around 80 people would initially benefit from the visas.
But according to the newspaper Le Monde, the French President, François Hollande, doubled that number in mid December, contrary to the advice of his government.
The French government will pay relocation fares and wave the visa costs.
Le Monde adds that, since September, French army officials and the French embassy in Kabul have received between 500 and 700 applications, and more than 120 of the requests have been processed.
Of these 120 applications, some requested to be relocated to another region in Afghanistan rather than moving to France.
In those cases, France would give the applicant at least 1,000 euros.
People whose applications are rejected will be given a severance pay “15 to 18 times” above the local annual salary, according to the paper.
The French embassy has also transferred applications from Afghans who wished to join family members in other countries to other embassies, such as the American, UK and German embassies.
The scheme had been in the works since 2011.
The last French combat troops left Afghanistan this month, leaving behind 1,500 soldiers working as trainers, logistic co-ordinators and doctors for local Afghan forces.
More than 100,000 soldiers, two-thirds of them American, remain in Afghanistan as part of NATO’s international coalition force.
Most of the soldiers will leave the country by the end of 2014.