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The findings, by TNS (in French), contrasted with its survey among Britons, which found that 41% supported remaining within the 28-member bloc, compared with 43% in favour of leaving.
The UK holds a referendum on 23 June on whether it should stay in the EU or leave.
In its poll results released on Tuesday, the Pew Research Center found a majority of people were unfavourable towards the EU in Greece (71%) and France (61%).
That followed a steep decline in EU favourability in France (down 17 percentage points from 2015 to 2016) and Spain (down 16 points over the same period). In the UK, support was down eight points, and in Italy six.
In five of the six nations surveyed in both 2015 and 2016, it found favourability had declined.
Here's a video explaining how the EU works in less than two minutes
This year, the poll surveyed 10,491 respondents in 10 EU nations from 4 April to 12 May - nations accounting for 80% of the EU's population and 82% of its GDP.
It found the strongest supporters of the EU were in Poland (72%) and Hungary (61%) - compared with just 27% of Greeks, 38% of French and 47% of Spanish.
In Monday's TNS poll, Germany was the country where the greatest number of respondents felt the UK should remain within the EU - 79%, compared with 15% who felt it should leave.
How Eurosceptic is the European Parliament?
EPP - European People's Party (centre-right)
S&D - Progressive Alliance of Socialists and Democrats in Europe (centre-left)
ALDE - Alliance of Liberals and Democrats for Europe (liberal)
GUE/NGL - European United Left-Nordic Green Left (left-wing and Eurosceptic)
Greens/EFA - Greens/European Free Alliance (Greens and regionalists/nationalists)
ECR - European Conservatives and Reformists Group (right-wing)
EFDD - Europe of Freedom and Direct Democracy (Eurosceptic)
NI - Non-attached (stands for "non inscrits" - MEPs not in any group, includes many Eurosceptics or anti-EU)
In Finland and the Czech Republic, 62% supported its continued membership.
A majority of respondents in the 10 countries surveyed in the latter half of May believed the economic situation in Europe would deteriorate if Britain left, except in Germany, where a majority felt it would remain the same.