The study, carried out with industry magazine Vêtements made in France, asked participants what their preferred ratification method was for the treaty.
Of the respondents 52% said they wanted a referendum, compared to 38% who wanted it to pass through parliament, and 10% who were unsure.
By contrast, 68% of the electorate of Jean-Luc Mélenchon, the leader of Left Front that includes the Communist Party of France, 72% of the Front National, and 43% of voters from the UMP, the party of former President Nicolas Sarkozy, said they would prefer a referendum.
For those on the right, "this will embarrass François Hollande", said the director general of OpinionWay, Bruno Jeanbart. The French president prefers passing the treaty through parliament, and has said that he is opposed to its ratification until a growth pact is agreed with other heads of state in the European Council.
What is more, 55% of voters from his Socialist Party included in the study said they wanted a referendum.
The leader of the far-right Front National, Marine Le Pen, was quick to react. In an address published on the same day as the study (24 July), she said a referendum was "required", also launching a petition in which she called for the public to vote no.
For Le Pen, daughter of Front National founder and staunch eurosceptic Jean-Marie Le Pen, "the treaty transfers budgetary sovereignty to Brussels technocrats" and would create "a German Europe ... a diktat of the privileged caste and the banks".
She continued: "Worse, it will require [the French] to pay the debts of other countries", without mentioning that plans to support Greece and Ireland were based on loans.
In the study, 53% of participants said they would vote yes to the treaty in a referendum, and just 20% would tick no. Of Le Pen supporters 48% would vote yes and 38% no, and of Mélenchon supporters 48% said yes and 34% no.
But Jeanbart said these figures must be taken with a pinch of salt. In 2005, two-thirds of French said they were still in favour of the European constitution as it stood, only to reject it in a few months later. What is more, most of the OpinionWay study participants said they were unaware of the details of the treaty, which has yet to fully enter into public debate in France.
"If a referendum was organised, the yes vote would not score so highly," said Jeanbart.