PARIS (AFP) - Thousands marched through Paris on Sunday in a "Day of Anger" against embattled President Francois Hollande's policies, including his decision to legalise gay marriage.

The protest called by a motley group of some 50 small and mainly right-wing organisations however failed to attract bigger anti-Hollande movements.

Organisers claimed a turnout of some 120,000 people, however police estimated there were 17,000 people at the protest, held under pouring rain.

The demonstrators called for a repeal of last year's law allowing gay marriage - one of Mr Hollande's campaign pledges - and made a slew of other demands.

Some called for France's withdrawal from the European Union, a demand of the Eurosceptic right-wing National Front party, while others urged the respect of freedom of speech, a reference to the government's decision to ban a show by a controversial comic whose sketches have been deemed anti-Semitic.

Many in the crowd complained about Mr Hollande's tangled love life a day after the President announced his split with his partner Valerie Trierweiler following an affair with a younger actress.

"There are enough scandals about the president, he is bringing dishonour to France," a 60-year-old woman who only identified herself as Marion, told AFP.

"You are here to say you are fed up," an organiser told the crowd, adding that France's leaders "are more preoccupied with their affairs ...than unemployment".

France, the euro zone's second-largest economy, is battling huge levels of unemployment. Hollande recently announced plans for 50 billion euros (S$87.4 billion) in spending cuts between 2015 and 2017 to revive the economy.

Several parties and organisations such as the far-right National Front did not take part in the protest.