Make sure you have all the roadside safety equipment when driving through France e.g. a disposable NF compliant breathalyser and others (bulb kit, fuse kit, warning triangle, visibility waistcoat, GB sticker, etc.). The porbability of getting stopped checked is less likely if you take the motorway.
What to bring in case of a breakdown, apart from the above usual bits and pieces. A big factor of what to bring in terms of parts is the condition of the car. If it has been maintained well, the journey should be fine.
As David says, you should have the equivalent of the V5 or proof of ownership and insurance. The French will require these documents if you get stopped.
Have a safe journey and enjoy the car!!!