Is it possible to drive from Calais to Paris without paying tolls? Well, anything’s possible but it will take 5 hours plus even without breaks and you’d have to stop on a journey that long so it would be more like 6 hours, I guess.
That route would be A16/A28 or maybe you could opt for the slightly more complicated A16/D901 or A16/D1001 but both of those would be 5.5 hours.
Time wise though the chances of you reading this and me giving you an accurate time is almost impossible as it all depends on so many variables such as, when you go, how you drive, whether it’s rush hour, peak holiday season, etc etc.
However, don’t expect to do it in less than 3 hours unless traffic is very good and you don’t stop at all along the way.
Personally, I would need at least one comfort break on a three hour trip and if you are taking children in the car then 2 short stops might be your best way to tackle it. That means you are going to be three and a half if not four hours depending how leisurely your break(s) are, and traffic conditions.
Remember if you are going during July/August the traffic can be very busy indeed, especially over the weekends.
Toll Charges are subject to change, so I don't want to put an actual figure here or I'll be burdening myself with keeping it up to date every-time they go up. The link I give at the bottom of the page will help and you can also see the page on Tolls in France