Hi Jennifer.
Mand's DH here, wheeled out for the usual French travel query!
Where in the Dordogne are you going?
Traffic in general going South could be a bit heavy, but it's not one of the really bad French summer weekends ( www.bison-fute.equipement.gouv.fr/fr/IMG/pdf/Traffic_forecasts_for_2010_cle1dc317.pdf )
In any case Paris is best avoided on Friday evening at any time of year, especially if you're not experienced in doing it and have small children in the car. The extra 30 minutes via Rouen is well worth it, the route is A16 / A28 to Rouen (very lightly used motorways until Rouen) a bit of navigation needed through Rouen itself (still on m/way / dual carraigeway but with a couple of junctions to watch out for- follow signs for Paris A13 m/way.) After a few miles on the A13 take A154 to Evreux which turns into the N154, then follow the signs to Dreux which you go round on a bypass by following signs to Chartres, then you go round Chartres on the bypass following signs to Orleans. I think it's actually signed Orleans all the way form Evreux, and it's all the N154 so pretty easy really. This then meets the A10 North of Orleans, from where you take the A20 all the way down to the Dordogne.
As far as staying goes you won't go too far wrong with any of the French chains, though the cheaper ones can be quite basic, you get what you pay for. The Accor website www.accorhotels.com/gb/united-kingdom/index.shtml is a good place to start as they own several brands (Ibis, Novotel, Etap, Formule1 etc.) so they are all on the same website. Campanile www.campanile.com/en/default.aspx & Kyriad www.kyriad.com/en/hotels/index.aspx (again one group - but 2 websites this time!) are also generally OK in my experience. If you want to be a bit more adventurous try Logis de France www.logishotels.com/en.html Independant but all meeting the Logis standard, more 'real' French and not necessarily any more expensive. Or if you want somewhere special try Sawday's website:www.sawdays.co.uk/
My advice would be:
1 work out roughly where you want to stop (difficult to judge as I don't know where in the UK you are coming from, but Rouen, Evreaux, Dreux, Chartres, Orleans for example might be about 1/2 way?)
2 use the hotel websites shown above to find hotels near your target town (or Google maps - just google 'Hotels + Townname' and a little map will pop up in the results, click on it and you'll see lots of red dots where the hotels are, you can then navigate round it just like Google Earth to find the ones near the bypass)
3 find a hotel near your route and not in the Town centre (many of the chain hotels are in retail park/industrial estates on/near the bypasses / motorways, sounds like that would suit you better) that is in your budget and has a family room (not all do)
4 do a quick check on trip advisor www.tripadvisor.co.uk/ (best overall hotel review website) and booking.com www.booking.com/(most reviews, especially for European hotels) to make sure it's not a total dump (you're not looking for rave reviews, just not loads of bad ones) then
5 book it up directly with the hotel website.
Enjoy!