> My problem is that they want to enforce this law worldwide
The point really is: how to protect or remedy against the privacy infringement felt by someone in France's jurisdiction? And what the EU Court is saying at point 72 is: EU law does not prohibit the French judge from finding that it is necessary to have a stringent measure, i.e. to order a search engine to really prevent infringement even if coming from outside the EU.
We live in a global, connected world. This goes both ways if you want effective protection of rights of individuals. The only concern here really is to protect an individual's right to have a bit of control over the information about themselves that are so easily made available by serach engines.
> Hypothetically, if EU law says their ruling applies worldwide and Google stops doing business in the EU, does that mean they would be exempted? Can they then show all results or does the EU still try to charge them with breaking their law?
The rules are different between the previous law and the GDPR. The GDPR will apply to a company which has no business in the EU, if the data processing activity relates to:
"(a) the offering of goods or services, irrespective of whether a payment of the data subject is required, to such data subjects in the Union; or
"(b) the monitoring of their behaviour as far as their behaviour takes place within the Union."