Châteauroux, it's ChâteaUroux
I live around 60km south of there, 100km north of Limoges and reckon 6 hours to Limoges with kids is a tough tough ask. More like 7. It takes me 5 1/2 hrs to get to Calais on my motorbike!
I would also agree about avoiding Paris; you can get lucky and get around with no problem but it's pot luck. The Abbeyville, Rouen, Evreux, Dreux, Chatres, N154, A10 route is my favoured way back down here, especially now the though N154 works have been completed. Going back, I have taken the A10 through to Paris and skirted east on the A86 to pick up the A1 but that was on the mbike.