One widely cited study by Pew from 2010 showed estimated that France had 4.7 million Muslims. At 7.5 percent of the population, this meant France had the largest Muslim population in Western Europe (for reference, in the same year Pew estimated that the Muslim population in the United States made up 0.8 percent of the total). Other estimates vary from around 5 percent to 12.
French census data can't tell us where France's Muslims live, but some past studies have put the percentage of Muslims in Paris as high as 15 percent. What census data can show is that around 9 percent of the population around Paris is made up of non-EU immigrants, though that number is likely influenced by other factors as well (Paris is a major international city, of course).
Whatever the actual size, France's Islamic minority has become a subject of concern and sometimes fear-mongering. One online poll conducted by Ipsos Mosi last year found that the average person in France thought that Muslims made up 31 percent of the population in the country, rather than 7.5 percent. As political scientist Steve Saideman puts it on his blog: "It is important to understand the real numbers, as fears of swamping generate or exacerbate xenophobia, and in pretty much every case, the populations of Muslims are so small that they are politically powerless."
And when it comes to levels of extremism within France's Islamic community, attitudes are again hard to ascertain. One recent poll suggested that 1 in 6 French citizens supported the Islamic State militant organization. When examined closely, its findings seemed incoherent and possibly flawed. (Incidentally, the earliest indications suggest that the Charlie Hebdo attack was carried out by al-Qaeda followers, who now see themselves as rivals to the Islamic State).
A more reassuring poll from 2006 found that 73 percent of French Muslims were "somewhat" or "extremely" concerned about the threat of Islamist extremism. In 2011, Gallup found that 56 percent of French Muslims felt Western societies "respected" Muslim societies. Given the variety of different backgrounds French Muslims come from, attempting to singularly define their positions may ultimately a difficult, even impossible task.
Perhaps most worrying in the current climate has been the relatively large number of French nationals who are believed to have gone to fight in Syria in 2014. Estimates put these at several hundred. You can see how that compares below (click for enlarged image).
France's Muslim minority may be disproportionately represented in some areas of French society (in 2008 it was estimated that between 60 and 70 percent of prison inmates were Muslims). It's worth remembering, however, that two of most famous victims of extremist terrorism in recent years were themselves French Muslims: Imad Ibn-Ziaten, a soldier shot dead in Toulouse in 2012, and police officer Ahmed Merabet.