Hi,
Outside of Paris this is the area of France I have done several extended stays, ie, more than 4 to 5 days. I would suggest Amiens or Arras. Both are connected to Paris by going to Paris Nord. Arras to Paris Nord on the TGV gets pricey but it's a 40 mins ride compared to 2 hours on the TER train. Both Arras and Amiens are good walking towns, ie, from the train station to the centre ville. You'll see that you just might be the only Americans going through the Arras centre ville. Canadian tourists go to the Canadian memorial at Vimy, from which it's best to reach by car from Arras. If your interest is WW1, northern France experienced the horrors of it...Amiens and the Somme valley, Cambrai, Arras, Albert, Frevent, Lens, Bethune, St Quentin, Perrone, etc. The big German memorial cemetery is there too in the next village.
True about the weather, it is cooler on the whole even in the summer relative to Paris. I like northern France, find it fascinating going through those towns and villages. See the beach towns along the coast of the Pas de Calais.