Asked whether they were in favour or against ending the Schengen accord which allows free travel within the EU, 67 percent of French people said they would back the move.
That figure put the French above the British, 63 percent of whom favour scrapping the Schengen agreement.
The Schengen zone comprises 26 European countries, 22 EU members as well as Norway, Switzerland, Liechtenstein and Iceland.
The accords are seen as a fundamental principal of the EU, but one which the UK never signed up to.
The IFOP poll, published in the Le Figaro, revealed Germans and Italians are keener to keep the borders open with only 53 percent of Germans wanting to close their borders and 56 percent of Italians.
The survey comes as subject of Europe's borders and the Schengen agreement is being questioned by many, especially those on the political right in France.
Both the far right National Front leader Marine Le Pen and Nicolas Sarkozy, who heads the centre-right Republicans have urged the old accords to be scrapped so France can retake control of its borders.
"Schengen must be immediately suspended and be replaced by a Schengen II of which member countries can only be a part if they previously agree to the same immigration policy," Sarkozy said previously.
"Europe is not meant to organise social and migratory dumping, almost systematically at the expense of France," he warned.
The high number of French people in favour of restoring passport checks at its frontiers could be explained by the tensions on its northern and southern borders.
In Calais around 3,000 migrants are camped out in the hope of making it across to the UK, where they believe they will have a better chance of gaining asylum and finding work.
They are unable to travel freely to the UK because Britain still maintains its border with France and since 2003 it has been installed on French soil.
The crisis has led to tensions between French and UK authorities, with some French officials calling for the border to moved back to Britain.
“Migrants belong in the country where they come from. Of course, we can be sensitive to the plight of migrants, but first I see the plight of people from Calais," said the National Front's Marine Le Pen, who called for France "to take back control of its borders".
In the south of France there has also been tension along the country's border with Italy where thousands of migrants cross over on their way to northern Europe.
Last month France effectively restored its border checks and refused to allow migrants to pass.
That led to migrants camping on the Italian side and provoked a very public row between French and Italian politicians.
But for the moment the Schengen agreement appears here to stay.
Calls by France to change the rules so more checks could be carried out on suspected terrorists in the wake of the January attacks in Paris, fell on deaf ears in Brussels.