No, I think you are moving around much too fast.
Two nights in Barcelona will give you just about 1-1/2 days in a city that other travelers have had to rush through when they had four full days available. There are lots of popular sights in Barcelona that require tickets purchased in advance that generally tie you down to a specific entry time. You will have a lot of difficulty putting together a workable itinerary if you have only 1.5 days and are interested in the traditional sights.
Three nights in Arles is just a bit over two days for Provence. It's the sort of area where most people want to visit a number of towns. The usual recommendation is to rent a car in order to include places like Roussillon and Les Baux as well as Arles, Avignon, etc. By choosing destinations carefully, it is possible to have a nice visit to Provence without renting a car. In either case, two days would leave me very frustrated.
One night in Normandy will give you perhaps a few hours there on your arrival day (since you'll be traveling all the way from Provence) and a few hours there the next day before you leave for Paris. That will not get you to the D-Day beaches unless you are willing to take a late train back to Paris and can arrange to take a D-Day tour that drops you off at the Bayeux train station in time to take catch that train. You'll also need to figure out what to do with your luggage during the tour. I do not recommend simply driving yourself around. The beaches will look pretty much like any other beach. The van-tours offered by companies like Overlord will be much more informative. The driver/guides will cover a lot of sites in one day, far more than you could manage yourself. And dealing with a car-rental agency would take precious time you can ill afford.
Even if you had three nights in Paris (and that does make Normandy problematic), that's only two days there, which is...painfully short.
You just are trying to go to too many places. Getting to Normandy is a bit awkward since you cannot fly directly to the logical base for D-Day visits (Bayeux). Getting around Provence takes time. Barcelona and Paris need more time than you are allocating. I think you should drop at least two of those four destinations so you can enjoy the others.
Edited to add: I failed to mention that 3 nights in Madrid and one in Toledo isn't bad. I love Toledo (much more than Madrid) but still would consider not switching hotels for just one night. Or perhaps split the time 2/2 if you are not big art fans.
