Firstly, check out the sticky posting at the top of this board. If that doesn't help then read on......
Most EU policies provide 12 months legal cover but may not give you fully comp for all that time, or may load the policy anyway as you are not complying with the proposal where you probably said it was kept in your garage at your UK postcode overnight.
I suggest you do a search on the web for specialist insurers or buy any of the monthly car fan magazines where you will see plenty of ads from brokers who will offer you what you are looking for.
Dont confuse 'green card' with insurance cover, just tell the broker how you are using the car and ask for the cover you want, and be careful to say on the proposal form exactly where the car is kept overnight so thay can't use that against you later on.
Bon chance!