The Ifop study found 29 percent of those polled said sharia legal and moral code was more important than secular France's laws, while 60 percent wanted to see headscarf ban on girl students lifted.
Some 74 percent of those surveyed do not want re-run of 2012 presidential election when socialist leader beat former conservative president.
Some 86% of public back constitutional change to allow French citizenship to be taken from bi-nationals if convicted of terrorist offences.
Poll suggests Front National leader Marine Le Pen and niece Marion Maréchal-Le Pen could both lose in regions they scored highly in on Sunday.
Public opinion split evenly over role of Greece's prime minister but majority of French back right of Greeks to have referendum on bailout terms.
The Pew Research Center survey result is in stark contrast to the recorded doubling of acts against Muslims in the aftermath of the Paris attacks.
In BVA poll 55 percent said they would support French action in Syria compared to 64 percent who were against it in 2013.
Staging the World's Fair was the preferred project over the likely Paris bid for the 2024 Olympic and Paralympic Games.
Financial information company Markit said its latest poll showed France and Greece saw accelerating rates of decline at start of second quarter.
Survey suggests president of Front National would win first round of voting if election were held today - but lose in second round.
Poll says 72 percent hold favourable opinions of German chancellor, way above President Hollande's ratings which have sunk as low as 12 percent.
Just over half of French people polled want Britain to quit EU, with only 42 percent believing Brussels should take London's concerns into account.
Survey suggests Front National boss would win first round vote and trounce President Hollande in second round run-off - but not other rivals.
Survey by TNS-Sofres shows support for François Hollande is at lowest level ever registered by the pollster for a sitting president.