Hiya
We go back and forth between France and England with our English dog and our French cat a couple of times a year. We drive and then go by ferry. In the last few years it has become much less complicated. We just hand over their passports and then (but not always) they hand us the chip reader to scan each pet. Of course all their vaccinations are up to date.
We are given a special card hanger to hang from the rear-view mirror of the car, to indicate there is an animal on board. When you make your ferry reservations you pay extra for transporting a pet on board (although I can't remember if you pay from the UK to France). Your pet must stay in the car (without you).
If you do return to the UK, there are other requirements for worms and ticks, so be sure to read up.
It's all very simple, so don't worry.