The most direct route from the UK by cross-channel ferry is probably via Ouistraham (Caen) using Brittany Ferries. However, Le Havre (LDLines and, recently, Brittany Ferries) and St Malo (Brittany Ferries and Condor Ferries). In the Summer Brittany Ferries run a fast service to Caen and Condor to St Malo (from Poole). Be aware that Ouistraham to Passavant takes about 3½ hours and includes a cost currently of about €30. Note also that, if you book with Brittany Ferries, we are able to offer you a discount code: contact us before you book.
Of course you can get cheaper ferries from Dover to Calais. You will then have a 350 mile (estimated 5½ hour) drive in France, assuming you take the motorway. In this case you will need to take the cost of petrol and motorway tolls into account. You can, of course, contact the ferry provider direct but you may find it more convenient to use a ferry website (a sort of go-compare of ferries). There are a number of these around; we've used AFerry in the past and found them helpful.
There is a third possible route from Newhaven to Dieppe. I'm sure a company like AFerry could help here, too, and can provide up-to-date advice should routes change or new ones become available.