Whatever you plan, plan to finish in Paris so you aren't rushing back the last day before.
We have done several trips like this. We once did 5 nights in Normandy. You can see some of the stuff here:
We spent a night near Mont St. Michel, two in Bayeux (plus beaches) and two in Honfleur (plus Etretat.) We loved it and could have added a night and done St Malo or Rouen. https://janettravels.wordpress.com/category/normandy/
We once spent a week in Semur en Auxois and used that as a base for touring Burgundy. Love the beauty of this area. https://janettravels.wordpress.com/category/burgundy/ Burgundy is one of the more scenic areas of France.
WE have spent time in the Loire and that would be a nice area as well.
Alsace is easy from Paris -- we spent a couple a couple of nights in Strasbourg and there are many nice places in the area.
And if you have not thoroughly explore the Ile de France, there are literally dozens of cool towns, small cities and chateaux right in the Paris region. Here are a few: https://janettravels.wordpress.com/category/day-trips-from-paris/
We also love Reims, Rouen, Chartres, Giverny, Auvers sur Oise just to name a few easy day trips from Paris. You could easily spent 6 days going to a great new place each day while enjoying evenings in Paris.