I am traveling from Ashford (Kent, England) to Aix en Provence via Paris. In Paris, I have to get from Gare du Nord to Gare de Lyon. How much time will it take to clear customs at Gare du Nord?
Gare du Nord is a train station and does not have any customs. If you are coming to France on a train, there will maybe be someone on the train to check your Passport but that is it. When you arrive to a country on a train, there won't be any big hassle like at the air port, where a big bunch of people arrive at the same time.
If Eurostar is your mode of travel you should be passport/customs checked out of England. I've done ferry from England and Eurostar from France; all the checks were at the starting end. Should be off the train at Gare Nord, catch your connection to Gare de Lyon and away to Aix en Provence with no hassle from the tax collectors.