I haven't used the Narbonne to Calais service, but a few years ago I used the Strasbourg-Bordeaux service, and drove to Narbonne where I met my husband who'd had to work another day and was on the car-sleeper train without the car.
First of all, the cars are loaded onto car carrying wagons for each stop en route and then connected to the main train. During that time, you find your compartment in a separate part of the train which will be connected to the car-carriers before you settle off. You have time to buy refreshments for the journey (to be recommended because the bar/catering service is limited if at all there) and although you get a small bottle of water provided by SNCF, you may feel that you need more. You may also need to make up your bed - sheet liner and pillow provided ... which can be absolutely hilarious in a confined space with five other people! ... but can take up some time.
On arrival, you will have to vacate your sleeping compartiment and adjourn to the station restaurant for a continental breakfast (voucher provided) while your car is unloaded and parked ready for you to drive it away. This probably takes less than 2 hours - it just depends on how many cars need offloading on one particular train.
I found that the service was a great help - I too was a lone driver, and suffering from a health problem at the time so I couldn't drive the distance. I had a comfortable (but short) night, and the motor rail staff could not have been more helpful. I would certainly recommend it, even though it is somewhat pricey in abstract, but not that much more costly than petrol, motorway tolls and overnight accommodation. Go for it!