The immigrants (including the imams who preach jihad) were accepted on an assumption that they will join the society and become citizens just like everyone else is. That assumption was wrong. The least painful solution would be to undo the grant of citizenship... but many of the immigrants have no other citizenship at the moment, and cannot be sent anywhere. The EU has very few options left:
1) Do nothing. Suffer terrorism, whack a mole when you can, but the opponent's human resources exceed yours, and their population grows while yours shrinks. This will not work in the long term, and the nation will cease to exist as soon as the Muslim population gets numerous enough to control the country through the democratic mechanisms. (That's where another Pinochet might step in.)
2) Dedicate some part of your territory to the opponent. Let them have their own state there. Build a wall and guard that border. This is technically doable. Legally, it's borderline; Stalin exiled several nations for their behavior during the World War II. Today collective punishment is illegal, but this separation is not punishment - it's a grant of statehood. France will lose some territory, but then it will be rid of the unwanted people. Islam would be outlawed in France, probably.
3) Allow a civil war to start; let the population fight it out. The end result will be the (2) above, only with far more dead and with lasting hate between the groups. This development promises no advantage, especially if Islamists win the war.
4) Use methods that are universally recognized as unacceptable today, like genocide or forced deportations into faraway lands. Even if attempted, this is going to create a lot of backlash, unless done exactly by Machiavelli's recommendations. Technically, it's not very likely. Legally... it might work if, say, Islamists get a nuke and explode it in some important place. Then the whole world will donate a few more nukes to them, free air delivery.
These problems are not unique to France; they will be the burden of every country that has a significant number of radical Muslims.
Europe's got to deport, and so do we. Millions and millions. Show us how it's done, guys, our lives and our civilization are on the line. Tick-tock.
Forced deportation is going to have to come back into vogue, given the stakes for morally mistaken host countries. It's one thing to accept Marielitos or Hungarian refugees, or Hmong fleeing persecution and mass murder in Laos. Moslems are serpents and will kill you.
Ironically, if Hitler had just deported German Jewry (as a lot of German Nazis apparently thought he intended to do before the Wannsee Protocol was enacted) rather than sending them to death camps, then deportation might not have the "illegal" status it has now.
Removal of populations, fwiw, was pioneered by the Assyrian Empire, so it's not as if Syrian and Iraqi Arabs had never heard of it.