The shock poll will fuel fears that another member state could soon follow Britain’s decision to quit the bloc.
It suggests that the EU’s reputation has taken a massive hit from its slow vaccines rollout, which continues to lag behind Britain and the US.
President Emmanuel Macron is likely to face an uphill battle to convince voters to back his pro-Brussels views ahead of next year’s French election.
Separate polling ahead of the crunch ballot shows him lagging behind eurosceptic candidate Marine Le Pen.
France’s Europe minister Clement Beaune said: “There has been a long-standing French disappointment with Europe.”
His remarks come after repeat warnings from former Brexit negotiator Michel Barnier that France could vote to quit the EU unless the bloc learns lessons from the UK’s divorce.
The EU’s mishandling of the coronavirus pandemic has sparked fresh calls for a “Frexit”.
Leading campaigner Charles-Henri Gallois, of Generation Frexit, said: “The polling shows the reality – the EU managed the COVID-19 crisis terribly.
“With poor vaccination roll-outs and sluggish border controls, this crisis has highlighted it’s time to take back control.
“It’s an unfortunate situation but the EU is totally responsible. It’s time to Frexit.”
But anger over the Brussels project’s performance was not isolated to France, with half of Europeans deeply unhappy with the EU’s handling of the health crisis.
The EU-wide polling for the Eurobarometer, carried out on behalf of the EU Parliament, shows that 48 percent of citizens view Brussels positively.
That’s down two percent since last November, while the number with negative opinion rose three to 17 percent.
Pollsters Kantar suggested that shows the project is still “enjoying its highest approval levels in over a decade”.
They add: “The image of the EU in citizens’ eyes has not suffered significantly during the COVID-19 pandemic.”
But over a third of voters say their view of the bloc has become worse over the past year – up 10 points in the last six months.
Austrians are the most eurosceptic with just 34 percent holding a good opinion of the bloc, followed by France on 40 percent.
The Eurobarometer poll, carried out on behalf of the European Parliament, surveyed 26,669 citizens across the EU’s 27 states between March 16 and April 12.