Daniel Pipes (http://www.danielpipes.org/article/4323) offers several potential scenarios regarding the future of Europe. I encourage you to read the whole piece. Here is a short excerpt for each scenario:
Muslim Rule– To sum up: this first argument holds that Europe will be Islamized, quietly submitting to the dhimmi status or converting to Islam, because the yin of Europe and yang of Muslims fit so well: low and high religiosity, low and high fertility, low and high cultural confidence. Europe is an open door through which Muslims are walking.
Muslim Rejection– Or will the door be shut in their face? American columnist Ralph Peters dismisses the first scenario: “Far from enjoying the prospect of taking over Europe by having babies, Europe’s Muslims are living on borrowed time. … predictions of a Muslim takeover of Europe … ignore history and Europe’s ineradicable viciousness.” Instead, depicting Europe as the place “that perfected genocide and ethnic cleansing,” he predicts its Muslims “will be lucky just to be deported,” and not killed. Claire Berlinski, in Menace in Europe: Why the Continent’s Crisis Is America’s, Too, implicitly agrees, pointing to the “ancient conflicts and patterns … now shambling out of the mists of European history” which could well trigger violence.
This scenario has indigenous Europeans – who do still constitute 95 percent of the continent’s population – waking up one day and asserting themselves. “Basta!” they will say, and reclaim their historic order. This is not so remote; a chafing among Europeans, less among elites than the masses, loudly protests changes already underway. Illustrations of that resentment include the anti-hijab legislation in France, irritation over the restrictions of national flags and Christian symbols, and the insistence on serving wine at state dinners. A movement spontaneously developed in several French cities in early 2006 to serve pork soup to the poor, thus intentionally excluding Muslims.
Muslim Integration– Such optimism, unfortunately, has little foundation. Europeans could yet rediscover their Christian faith, have more babies, and cherish their own heritage. They could encourage non-Muslim immigration or acculturate the Muslims already among them. But such changes are not now underway, nor are their prospects good. Instead, Muslims are cultivating grievances and ambitions at odds with their indigenous neighbors. Worryingly, each generation appears more alienated than its predecessor. Canadian novelist Hugh MacLennan dubbed his country’s English-French split the “Two Solitudes“; one sees something similar, but far more pronounced, developing in Europe. Those polls of British Muslims for example, find that a majority of them perceive a conflict between their British and Muslim identities and want Islamic law instituted.
The possibility of Muslims accepting the confines of historic Europe and smoothly integrating within it can virtually be dismissed from consideration. Even Bassam Tibi, professor at the University of Göttingen, who has often warned that “Either Islam gets Europeanized, or Europe gets Islamized,” has personally given up on the continent. Recently, he announced that he is leaving Germany after 44 years’ residence there, to move to Cornell University in the United States.