I have just re-read your post and see that you are leaving the bike in France permenantly...
I will need to leave my GS in France from April this year
That changes my answer

Get it registered in France, Once registered you will not have to get it MoT'd or Taxed again and you will be free to ride anywhere in europe without worry.
If you can read French this document will help (or confuse you)
http://tinyurl.com/yhh5q4v but it is what the DRIRE and Perfectures work from...
This is the process to register a bike in France, May Vary in deartments but shouldn't now the Immatriculation is Nationale
VEHICLE REGISTRATION
1. Obtain forms from the Prefecture
DEMANDE D’IMMATRICULATION
2. Have vehicle checked with local Dealer – light adjustment, clocks, restricted power to 78.1Kw or 106bhp etc.
3. if it is a car you will need a ControleTechnic (like an MOT)
4. Take original and copies of all forms, V5C registration document, original bill of sale, proof of residence and passport to IMPOT to get QUITIS FISCAL ON CERTIFICAT DE DEDOUANEMENT (Tax form).
(** A Certificate of Conformity may be required should your vehicle not conform to EU standards (ie have a CE plate). This document is available from the manufacturer at a cost to you
5. Take all documents to Prefecture to collect Carte Grise. Take passport and EDF bill for identification. Payment depends on engine size.
6. Get number plates and insurance changed.
Happy Riding!
The Carte Grise is an important document and is valid for the life of the vehicle. It will need to be shown at garages when obtaining servicing/repairs, parts etc.
CERTIFICATE DE CESSION D’UN VEHICULE
This certificate is required should you sell or dispose of a french registered vehicle.