Can you drive from dieppe to the south of france avoiding motorways? ?

You sure can and even though it might take you quite a bit longer you can use this opportunity to view the real France and meet genuine French people and taste genuine French food. In case you are in a hurry motorways are the way to go but in case you have extra time smaller roads are quite nice and maybe less dangerous?

Sure but would take you too long.

i probably qualify as an expert traveling from uk to south of france ..my idea of south of france is perpignan rather than nice ..monte carlo etc ..lost count times i have driven around paris to head towards toulouse and beyond ..there are dozens of routes you can take but none will save you money ..i tend to drive through the night ..non stop folkestone ..paris ..toulouse ..perpignan ..12 hours ..yes i use toll roads ..but would take a lot more time and fuel on normal roads ..and frankly bore me 

Of course you can to do it, but it will take you more time. The good part at this is that you will see the beautiful landscapes, villages, etc ....

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I live in the South of France ( near Foix where there is a great medieval castle, called: Château de Foix / Foix Castle).

Yes, but it would take a VERY long time.