I'm not familiar with French tax law, but my sister works for Revenue Canada (now CCRA), and some of the principles would likely apply.
For example, tax collectors want money. They take property only if they can't get money, then they turn the property into money. So, assuming the ruling is upheld throughout the legal process and the Society refuses to pay voluntarily, the French government will likely sieze the Society's french bank accounts. If this yeilds a decent stream of cash, then they will get their money, sooner or later. Physical assets would be the secondary target. Since the Society owns all Kingdumb Halls (I am guessing around 500 to 1000) of them, there would be more than enough assets to go around. Foreign assets would be the last target, and success would depend on the skill of the person hiding the assets.
In some jurisdictions, when a person (or corporation) loses a case, they must pay the damages immediately. If they appeal and win, they get the damages back. In Canada, no payment is required if an appeal is pending. I'm not sure how France works. I suspect that this will drag out in court for quite some time to come.
With regard to the appeals, I'm not sure if taxation is considered an issue appropriate to the European Human Rights court. I would think that the nation of France would have ultimate sovereignty over their tax laws.
Siezing foreign assets is a difficult thing, unless the government can prove that the assets were moved specifically for the purpose of tax evasion. In which case, their should be fines and possibly charges levied. However, they probably have adequate French assets to satisfy the tax man.
Personally, I think that in the end, the Society is going to win this one. But it doesn't really matter. Between tax problems, pedofiles, shunned blood transfusion victims, lawsuits against elders, and deranged murdering disfellowshipping victims, the society is in one hell of a lot more trouble than they can handle.
If they fail to normalize and go mainstream, I don't think they will be able to withstand the drains (both in numbers and dollars) that are coming their way.