We always drove and used Channel Tunnel (neither DH or I like travelling by ferry). We always found this fine with DCs, they had DVD players and audio books and we would take regular breaks (French motorway service stations are much nicer places than British ones).
Taking our own car made packing much easier. No luggage restrictions plus we had a familiar car to drive once on site.
Some of the campsite companies eg Eurocamp allow overnight stops at campsites along the way. This added to the holiday as we would be able to stop for the night, use the campsite facilities (pool, playground etc) then move on the next day. It meant the journey took a bit longer but became part of the holiday.
We have used a few of the campsite companies plus booked direct with campsites. IME booking direct is cheaper but you can find the end of let clean is a chore you can do without with a journey ahead of you.
Eurocamp expect you to have washed up and we always do a sweep out but that is useful anyway for finding stray sock/toys/teddies which have put themselves under the beds.
Some campsites require a wrist band or similar to be worn when on site. A deposit is paid for this then returned at the end of the holiday.
If you havent been on a campsite holiday before then I heartily recommend it especially with young children. They generally have a shop, takeaway, bar, restaurant. In addition there will be playgrounds, swimming pools etc. In addition to your mobile home you will generally get outside furniture, some pitches allow for a bit of space for your children to play on. Campsites are family oriented and the rules are around everyone having a good holiday.
Some of our happiest holiday memories come from staying on campsites. DS at around 10 months old was fascinated by the badminton players who would use the roads as their courts. He would happily sit in his cot watching the games. Early morning walks round the campsite with early rising toddler DCs and spotting wildlife.