Hi Charity Claire, I did London to Paris via Dieppe last year, over 4 days. The routes I devised/used were very traffic free, amazingly so near Paris. Bits of the London Newhaven route were busy but as we left on a Sunday it wasn’t so busy. France cycling is just a dream, especially the routes we took.
Take a look at the routes on my blog: london-to-paris.winchcombe.org