Hi Andy,
Welcome
The logistics with a bicycle are not that different. You just can take a normal ferry and you put your bike in the lower deck between the cars. Best place is probably Dover but better check first. Wild camping is not allowed in France but if you start camping just after sunset nobody will bother you. If not try to ask the local farmers. Better start learning a little French as the French themselves don't (want to) speak English.
Should you decide to go by plane you can buy a
bicycle pyjama , basically a plastic sheet to protect your bike.
Cycle the world,
Marc