PARIS, Jan 6 (Reuters) - The French government has given Luc Remont, the new chief executive of EDF, six months to come up with a strategic plan for the debt-laden utility which shoulders the lion's share of the country's electricity supplies.

In a three-page letter signed by Prime Minister Elisabeth Borne and sent to Remont and dated Dec.9, the government asked him to hammer out a "new strategic roadmap" for operations and finances in the first half of the year. The letter, first reported by newspaper Les Echos, was seen by Reuters on Friday.

EDF, already majority-owned by the French state and in the process of being fully nationalised, is facing pressure after an unprecedented number of reactor outages, which reduced last year's nuclear output to 30-year low.

The company has net debt of over 40 billion euros weighing on its books. It is one of Europe's biggest utilities and is central to France's nuclear strategy, which the government is banking on to blunt the impact of soaring energy prices exacerbated by the war in Ukraine.

Borne in the letter said EDF should set new ambitious targets this month for improved nuclear output.

She called for budget discipline regarding new nuclear projects after EDF's next-generation reactor project in Flamanville suffered numerous cost overruns and delays.

The prime minister said she wanted the Flamanville plant to start producing energy in the second half of this year.

On Dec. 16, a week after Borne's letter, EDF said the Flamanville EPR reactor, already a decade behind schedule, was now expected

to start operations in the first quarter of 2024 and cost 13.2 billion euros

- an additional delay of at least six more months and a cost increase of 500 million euros from the last, January 2022 forecast.

When the Flamanville project was first announced in 2004, it was estimated it would cost 3 billion euros and would start operations in 2012.

Wary of the group's strained finances, Borne also told Remont to "target" EDF's investment policy and bring foreign activities "in line with the company's financial and industrial capacities".

The prime minister's office had no immediate comment. (Reporting by Benjamin Mallet, writing by Silvia Aloisi, editing by Richard Lough)