“We will be uncompromising and relentless,” warned Bruno Retailleau, the outgoing interior minister, adding that he had given police instructions to make arrests “as soon as there is the slightest slip-up”.
Jean-Luc Mélenchon, the leader of the radical left party France Unbowed (LFI), asked participants to the strike to be “disciplined”.
“Any violent actions would only serve one person – Mr Retailleau,” he said.
Ahead of the protests, Laurent Nunez, the Paris prosecutor, had expressed concerns that the demonstrations would be “derailed” by far-left groups and urged shops in the city centre to close for the day.
Thursday’s strikes come after around 200,000 people took part in protests organised by the grassroots Bloquons Tout (Let’s Block Everything) movement last week, which caused some disruption across France.
Bayrou’s unpopular budget proposal – aimed at bringing down France’s high public debt with €44bn (£38bn) worth of cuts – caused him to lose a confidence vote in the National Assembly last week when parties across the political spectrum united to topple him.
New Prime Minister Sébastien Lecornu, who is yet to assemble a ministerial team, has not entirely renounced the cuts and has held talks with opposition parties in an attempt to reach a compromise on the budget.
Lecornu’s position is perilous. Like his two predecessors, Bayrou and Michel Barnier, he faces a hung parliament divided into three blocs with deeply differing political leanings, making it difficult to craft a budget palatable to a majority of MPs.
But France is also staring down the barrel of spiralling public debt, equivalent to almost €50,000 per French citizen.
Barnier and Bayrou were also brought down as a result of their proposed budgets, which would have entailed substantial cuts – with politicians on the left instead calling for tax rises.
“Of course, we’d like more stability in government, but whether it’s Lecornu or someone else, we want workers to be truly taken into account,” trade unionist Alexandre Dubois told the BBC.
“And we need to move away from this logic of short-term economic performance.”
Additional reporting by Marianne Baisnée in Paris