On the eve of the anniversary of Hollande's May 6th win last year over right-winger Nicolas Sarkozy, the Communist-backed Left Front gathered supporters for a march starting at the Bastille, the iconic square of the French Revolution.
Many were also expected to gather for separate protests in Paris and other cities to oppose the government's plans to legalise same-sex marriage and adoption by gay couples.
The demonstrations come with polls showing Hollande as the most unpopular president in modern French history. Many voters are angered by an economy on the edge of recession and unemployment hitting a 16-year high.
Jean-Luc Melenchon, the Left Front's firebrand candidate in last year's vote, called the protest in Paris last month at the height of a scandal over Hollande's ex budget minister Jerome Cahuzac being charged with tax fraud.
Melenchon, who said he expected 100,000 to attend the rally, told the crowd the Socialist government had betrayed its supporters on the left.
"We do not want the world of finance in power! We do not accept the politics of austerity!" he told protesters waving the red flags of left-wing movements.
In an interview Sunday with newspaper Le Parisien, Melenchon called on Hollande to "return to the left, where he was when he was elected".
He accused Hollande of contributing to Europe's economic crisis by focusing on "the interests of shareholders, of big business and of European austerity policies, to the detriment of the workers."
Melenchon called for a government reshuffle with himself or Industrial Renewal Minister Arnaud Montebourg – considered one of Hollande's most left-wing ministers – as prime minister.
Opponents of gay marriage were meanwhile to rally in major cities in a bid to force Hollande to back down from signing a bill approved in parliament last month.
The bill, which is also facing a constitutional challenge, sparked months of demonstrations across the country, with some descending into violence.
It has been one of the most controversial reforms of Hollande's first year in office, with right-wing opponents demanding the issue be put to a referendum.
About 1,000 people protested against the bill in Strasbourg on Saturday and other protests were due Sunday in Paris, Rennes, Lyon, Montpellier, Toulouse, Dijon and Lille.
Sunday's protests follow another demonstration on Wednesday that brought hundreds of supporters of the far-right National Front to the streets of Paris, as a poll showed its leader Marine Le Pen would come second to Sarkozy if an election were held now, far ahead of Hollande in third place.
Since his election, Hollande's approval rating has fallen faster and further than any other president's since the founding of France's Fifth Republic in 1958.
The government has said it will hold a meeting on Monday to set its agenda for the months to come, with the focus on tackling unemployment, boosting economic growth and controlling public finances.