It appears that you will commit a criminal offence if you drive a car not registered in the EU, into an EU country without declaring it at customs. From what we understand so far, the rule has been in place for a while but either an exemption for hire cars has now expired, or the law is being applied more strictly.
Basically, you'll be treated as attempting to smuggle the hire car into the EU!
The regulation is reported to be worded such that "anyone domiciled in the EU must apply for a customs clearance and registration document before entering the EU with a car that does not have an EU registration", so if you're "domiciled" outside the EU then it doesn't apply. Thus, in a slightly bizarre twist, this regulation won't apply to British renters following an exit of the EU. :?:

The Law IS being applied
The Local (Swiss news site) has a story (from 2014) of a "German pensioner who was fined €15,000 for driving a Swiss car across the border into Austria". The article (click here) states that "cases like this are unfortunately not rare" and ends with the following advice from ADAC (German motoring association) :-
ADAC wrote:We advise drivers who rent a car in Switzerland to ask for a car which is registered in the EU if they wish to cross the border with it
LeNews has more on this story here :- http://lenews.ch/2014/06/19/drivers-beware-hefty-fine/
Latest News
There is ongoing confusion regarding the regulation and whether or not, for example, the French authorities are to apply it.
There are discussions, with recent experiences being related, on the following forums :-
- At UK Climbing
- On Snowheads here and here.
Swissinfo.ch, in this related article, reports :-
Swiss Government wrote:On June 13, Swiss Finance Minister Ueli Maurer confirmed that recent EU legislation had removed the previous eight-day grace period for driving a car rented in Switzerland within the 28-member European Union. He said that the Swiss government is working on solutions to the issue with the EU but that in the meantime, car hire companies have been offered the option of purchasing and registering cars in the EU specifically for use outside Switzerland.
...however...
Swiss Customs Administration wrote:France's application of the law could be different than Germany or Austria's
Anecdotally
Reaction of car hire companies, and advice from border agencies, appears to vary from "no problem" to "we don't know either" :-
- Avis are attempting to provide EU-plated vehicles in Switzerland.
- Austrian customs advice appears to say 8 days exemption for a Swiss vehicle.
- At least one report of a Swiss hire car being stopped at the French border (non-EU driver so no problem).
- Dollar have told one hirer there's no issue.
- Alamo have refused pre-booked cars at the Swiss side (GVA) and sent customers to the French side.
So, a somewhat confusing situation to say the least.
In essence, for reasons that are not at all clear to us, the EU has decided to criminalise something that a few million people have been happily doing without a care over the past few decades.
We'll update this post as more information becomes available, and we certainly hope all will be clear by the winter!
If you've got any current personal experience (of renting a Swiss hire car) then please do let us know here... :shock: