The move comes as President Francois Hollande's government seeks to limit executive pay at companies in which it is a shareholder.
Finance Minister Pierre Moscovici said the government, which holds a 15 percent stake in the loss-making airline, would voice its objection to the bonus at a shareholders' meeting.
"The state representative will vote against (the payment) and I hope that other shareholders will follow suit," Moscovici told France Inter radio.
"Morality dictates that Pierre-Henri Gourgeon himself reimburse this," he said.
At the start of the meeting, current company chief Jean-Cyril Spinetta said the bonus would probably be rejected but that Gourgeon was under no obligation to return it.
"Given the position expressed by the state shareholder, it is quite likely that it will be rejected," Spinetta said.
But he added that "the commercial code is very clear.... The rejection, if it takes place, will have no direct consequence on the compensation he has received."
Gourgeon was appointed CEO of the airline in January 2009, but resigned in October amid rising losses. Air France-KLM reported a net loss of 809 million euros last year, compared with a net profit of 289 million euros in 2010.
The 400,000 euro bonus for Gourgeon was part of a 1.4 million euro severance package awarded after his resignation.
Hollande has vowed to limit the pay of top executives to no more than 20 times the lowest salary in a company at firms where the state is a majority shareholder and to encourage shareholders to push for the same limit at companies where it holds minority stakes.