Last month with the Charlie Hebdo killings, something that got overlooked was the release of a book by French author Michel Houellebecq set in a near future where France is ruled under Shariah Law(TM).
There were many outcries, some defending the book (under free speech), some attacking it for fearmongering and playing into the ideologies of the far right.
But not many seem to have actually asked the question over how accurate it would be and what would a French state under "Shariah Law (TM)" actually be like.
Granted that as it is a work of fiction, it does not need to match any reality out there. The question is less if the book is accurate and more what would a European country with a majority non Muslim population be like under "Shariah Law (TM)".
First thing that would surprise many is that there is not a "Shariah Law(TM)". Shariah means "the way" and is about the philosophy and methodology in lawmaking.
There are many books on Islamic jurisprudence and are from different schools of law but they differ in methodology depending on the school of law they followed and much would not be about civil law but about personal law - something that is not implemented by a state.
Further, rulings in Islamic Law are not as opaque and powerful as those from Christian authorities. While a Christian authority would position its position as the "Will of God", in Islamic law the judge would not be so presumptive - his view is an opinion based upon his understanding of the source material and is not considered beyond reproach.
If true Islamic law was ever implemented in Europe, the first issue would be that it would only apply to Muslims and there would need to be a civil code that applies to everyone including non Muslims.
Rules on Hijab
Firstly, no everyone wont be covered up. The Islamic rules of Hijab apply to Muslims. I do not know if historically there has been any civil punishment for flouting them, or whether it has been left as a family matter.
In either event, the Islamic rules only apply to Muslims and the historic response to others not following the rules is to avert our gazes.
Will alcohol be banned? no. Non Muslims are allowed to drink. In early Islamic times, any puiblic display of drunkenness was punished so as to not allow it to spread.
Haraam Food / Pork
Islam does not prohibit non Muslims from consuming haraam food. However it does demand protection for animals and prevention of cruelty, so dishes where eg living fish are eaten could be banned.
Would everybody be forced to study the Qur'an and/or arabic? no. This has never been forced on anyone, not even Muslims.
Would the sciences be verbotten? no, unlike the Christian churches, Islam has always placed greater importance on science and it is understood as a way to learn more about God's creation.
Freedom to practice other religions
Would christians have to convert to Islam or go into hiding/be killed? No. This has actually been something that is almost uniquely christian with events such as the reconquista/spanish inquisition, reconquest of sicily and loss of eastern european lands (Bulgaria and others) to Christians in the 19th centur where being Muslim often meant a choice between hasty exile or a death sentence.
Would this be banned? no. While some call the document promising to protect christians in the Yemen a forgery, it is no doubt a historical document and is alteast centuries old.
While the Islamic ideal is that leadership should be given to those that do not covet it, according to some historians, when it came the time to choose the third caliph, the adults of madinah were "polled" to decide who should become the third caliph.
These are not new historians and even if their accounts are discounted, the idea of polling for leadership is not one that is against Islam.
Some argue that electing a leader is allowed, but there is no Islamic history setting term limits. But we know from the nomination of the second Caliph that adding conditions to leadership is allowed - Caliph Umar (ra) who had not even wanted the ridaa wars to take place was given the condition that the fight against the Persians over Mesopotamia must not be abandoned.
Tax / Jizya
Would all non Muslims have to pay another tax for being non Muslim? Not neessarily.
To expand, it needs to be explained that Jizya is meant as a protection tax - a tax which in return gives the state's protections. It applies to those that are unwilling to take part in the states affairs.
I have read previously that in arabia there was a tribe of non Muslims who agreed to take part in Muslim afairs of state, fight along with Muslims but not pay the jizya and they were allowed to do so.
This shows that there is no need for an extra tax and it is perfectly valid for contributing citizens not to be treated differently based upon faith.
For other taxes, most are there to provide a service and the historical example used in Muslim books of charging the beneficiaries of a canal system for its building/upkeep would apply.
Would everyone be forced to pray?
There is a verse in the qur'an condemning those hypocrites that pray only to be seen as worse than the non believers. I would suggest that any saudi-arabia style public enforcement of prayer times etc would not apply this verse in the best possible terms.
What would change?
The system would only need to be changed to allow Muslims to practice Islam within the law. Any laws banning the hijab would need to be revoked and some might cry at this but the banking system would need to be changed to allow Muslims to have interest free banking and limit speculation.
There would be other changes as society demanded them, but the idea of forcing non Muslims to comply with Islamic law is alien to Islam.