Vehicles travelling in mainland Europe must carry their registration document. An exception is made for vehicles on hire, where for obvious reasons the rental / leasing company will not want the registration document to be carried in the vehicle.
In this circumstance a Vehicle on Hire certificate must be carried. It contains details of the vehicle taken from the V5, along with the name and address of the hirer and enables the authorities to verify that the person driving the vehicle has permission to do so. Photocopies of the V5 or letters of authority are not accepted. The BVRLA provides VE103B certificates to its members.
Speak to your rental or leasing company, who you will need to seek permission from to take the vehicle abroad and will advise you on the documentation / in-vehicle accessories needed when driving a vehicle abroad. Though ultimately the responsibility to ensure you have everything you need lies with you, as the driver of the vehicle.