You have asked whether a vehicle belonging to a UK keeper, who has a French holiday home (temporary residence) may register the vehicle in France, and use the vehicle to return to the UK for occasional short visits. 

The International Circulation Order that governs where an individual must register a vehicle makes it clear that each person should only register in the Member State of the person’s normal place of residence (country of permanent residency). Article 7 of Directive 83/182/EEC and Article 6 of Directive 83/183/EEC set out rules for determine normal residence, in situations where the person concerned are temporarily or permanently living and driving in a Member state other than their own. 

The European Court of Justice has also set out a criterion that permanent residence is taken to be the place where a person lives 185 days per year. 

This means that as an UK resident a person cannot drive a foreign registered vehicle in the UK. If the normal residence for the individual is the UK - the keeper is legally required to register in the UK (not in the country of temporary residence, in this case France) 

The direct.gov website makes it clear that UK residents cannot use a foreign registered vehicle on UK roads. The only exception is where a UK resident is employed or self-employed in another EU member state and needs to drive a foreign vehicle on a temporary basis. 

If a UK resident is stopped driving a foreign vehicle in the UK, it would be for them to demonstrate they are legally allowed to do so.