PARIS (REUTERS) - Francois Hollande's distant prospects of winning a second term as French president were further dented on Monday when a poll suggested he would not even win the endorsement of his own Socialist Party's supporters.

Opinion polls have for many months shown Hollande losing the May presidential election to all likely adversaries, but the new poll pointed to him being defeated in the party's candidate selection process by former industry minister Arnaud Montebourg.

Montebourg, 53, who made his mark by espousing a markedly leftist line, announced on Sunday that he would take part in the January pre-selection contest.

The BVA-Salesforce poll, conducted from Sep 13 to Sep 20, showed him winning the left-wing primary with 52 per cent of votes versus 48 per cent for Hollande.

The 62-year-old Hollande is France's most unpopular leader in modern history and has yet to declare his intention, but is expected to do so in December.

The election is likely to come down to a second round battle between the centre-right party ticket - most likely former prime minister Alain Juppe or former president Nicolas Sarkozy - and far-right National Front leader Marine Le Pen.

Montebourg made his mark in 2011 by winning a surprisingly large 17 per cent of votes in the primary where Hollande secured the Socialist Party ticket, after which he went on to beat Sarkozy in the May 2012 ballot.

Despite a remit to help secure a renewal of industry and stem a haemorrhage of industrial jobs to lower-wage countries in eastern Europe, Montebourg's ministerial term in Hollande's government was marked by several high-profile factory closures.

He has not always spoken kindly of the president. When Hollande's now former partner, Segolene Royal, was running for president in 2007, Montebourg, her spokesman at the time, famously said Royal "has only one flaw - her companion".