Houellebecq is a pessimist about human nature. It's never been clear to me how much he agrees with his characters' self-pitying diatribes against modernity or their longing for the carnal comfort of women as sex objects. In Submission the men submit voluntarily, at least as far as we see, though we may question how voluntarily the women submit to new rules limiting their participation and self-expression in public. The most I can say is that, not having read all his novels -- Submission is the fourth I've finished -- I don't recall anyone representing or articulating more radical alternatives to the hypercompetitive modernity decried by so many of his characters. In passing this time, his characters dismiss the left as nihilistic. Leftism is a hopeless cause at a time when people seem to be longing for a haven in a heartless world, as Marx might have said. In this environment, Islam has two advantages. First, Muslims have as supposedly unbreakable a cultural solidarity as the Chinese. Second, and crucially for French converts, it promises happiness through submission, a concept readers of that popular French novel Story of O can appreciate. Here's a French convert making a pitch to our narrator.
...for me, there's a connection between woman's submission to man, as it's described in Story of O, and the Islamic idea of man's submission to God. You see, Islam accepts the world, and accepts it whole. It accepts the world as such, Nietzsche might say. For Buddhism, the world is dukkha - unsatisfactoriness, suffering. Christianity has serious reservations of its own. Isn't Satan called 'the prince of the world?' For Islam, though, the divine creation is perfect, it's an absolute masterpiece. What is the Koran, really, but one long mystical poem of praise? Of praise for the Creator, and of submission to his laws.
Again, you can guess that Houellebecq (as opposed to his character) sees a point to this without agreeing with much else in the argument. The author, after all, once called Islam the stupidest of religions and was tried for it in a French court. He more recently conceded that he could fairly be called an Islamophobe, while emphasizing that, for him, that really meant fear rather than hatred. My hunch is that Houellebecq feels the temptation to submit -- to surrender autonomy or responsibility in return for assurance and comfort -- but resists it by writing about it with often pornographic honesty and ugliness, while applying the same satiric touch to the culture that provokes the temptation. In his own way Houellebecq is as much a prophet as Muhammad was, if not more so. I don't mean that he claims clairvoyance for his novel, but that like many a prophet, if not like Muhammad, he comes to warn and denounce. In Submission the warning is only indirectly about Islam; the real target is a culture that was destroying itself long before Muslims joined in.