The EU does have fairly strict "limits" for NOx emissions from diesel vehicles. The affected VW models, along with many other diesel vehicles, are known to
far exceed these limits in real-world driving.
However, legally the cars are only required to meet emissions limits in test conditions, and the rules allow for emissions control devices to be disabled if necessary "to protect the engine". So it's not clear if any laws were broken by Volkswagen's use of a defeat device.
If there are to be any successful lawsuits against VW over the emissions scandal in the EU, they will likely relate to consumer law - i.e. that VW's cars were deceptively sold as being clean when they were not, and people's vehicles lost value due to VW's actions when the emissions problems became known.