By Inti Landauro

PARIS--The French government suggested selling Areva's unit that manufactures, installs and services nuclear reactors to French state-controlled power utility Electricité de France SA in a bid to rescue the loss-making nuclear engineering firm and restructure the industry, Areva's Chief Executive Officer Philippe Knoche told union representatives in a meeting on Thursday.

Mr. Knoche told the union representatives that the government was evaluating a partial or total sale of Areva NP, which handles the company's core business, to EDF for an amount still to be determined, said Jean-Pierre Bachmann, the representative of the CFDT union, who attended the meeting. Mr. Knoche also said other options were discussed, an Areva spokesman said Friday.

The government proposal is the latest in a long-standing struggle to keep France's nuclear sector afloat after bad investment decisions and changing international attitudes toward nuclear power, notably after the Fukushima disaster in Japan in 2011, have pushed Areva deep in the red.

The meeting between Mr. Knoche and the unions was held after French Economy Minister Emmanuel Macron said he was asking EDF--the operator of France's fleet of nuclear power stations which provide most of the country's electricity--to come to the rescue of Areva by deepening their industrial and possibly financial ties.

A solution will be found for Areva by the end of the month, a spokeswoman for Mr. Macron said Friday.

EDF and Areva, which are both majority-owned by the French state, have to cooperate better over the construction of nuclear reactors and tendering for international business, Mr. Macron said Thursday.

A spokeswoman for EDF declined to comment.

Areva is currently working on a plan to sell assets, cut costs, reduce capital expenditure and start talks with unions over possible job cuts.

The unions oppose the sale of the nuclear reactor business, which represented almost 40% of its overall revenues in 2014. "Areva would be left without its core business, it wouldn't be able to make reactors or even design them," Mr. Bachmann said. "Additionally, the company provides equipment and services to some of EDF's competitors, how would that be possible after a sale," he added.

Unions will oppose such a plan and will propose an alternative, he said.

Write to Inti Landauro at inti.landauro@wsj.com