Former French foreign minister Laurent Fabius will step down as president of COP21, the UN's climate forum, after being appointed head of France's constitutional court, according to a resignation letter seen by AFP.

Fabius wrote on Monday to President Francois Hollande "to tender (his) resignation" as head of COP21, a post in which he helped to steer the troubled UN climate talks to a successful conclusion in Paris last December.

Fabius, 69, had expected to stay in the one-year post until November but drew flak in the French political arena for seeking to hold on to two demanding jobs at the same time.

COP21 stands for the 21st Conference of the Parties (COP) under the UN's Framework Convention on Climate Change (UNFCCC).

Fabius played a key role in sealing a historic deal under which the 195 UNFCCC states pledged to curb greenhouse-gas emissions to keep global warming to under two degrees Celsius (3.6 degrees Fahrenheit) over pre-industrial levels.

Taking effect from 2020, the accord will also channel hundreds of billions of dollars in help to poor countries that are most exposed to climate change.

It was seen as the jewel in the crown of Fabius' long career, which saw him appointed France's youngest-ever prime minister at 37.

In his letter to Hollande, Fabius said: "You gave me the honour of approaching me to preside over the Constitutional Council, and I thank you deeply for this.

"In my opinion, there is no incompatibility (between this post) and the presidency of the last phase of COP21.

"However, given the beginnings of an internal controversy on this subject, I find it preferable to tender my resignation as president of the COP."

The COP, the supreme decision-making body of the UNFCCC, convenes at ministerial level once a year. The presidency is taken up by the country which hosts the big annual gathering.