Giverny and Rouen are feasible Norman day trips from Paris (even one day for both if you are nimble). Further afield, such as Bayeux and Mont St. Michel, should really be overnight. There are other fine day trips from Paris, of course.
As for the rest of it, I think you'd shortchange yourself unless you can add at least a few more days. That is, while this is feasible, you might enjoy better a trip that covers less ground but lets you see more of that ground.
A road trip to Annecy from Paris could be charming, with stops along the way. Since you do not have time for that consider a train, perhaps to Chamonix first. Trains are often faster than driving in France.
Avignon is not really at the coast, though it's not so far that you could not detour that way if you had time. Annecy, or Chamonix, to Barcelona is really an all-day proposition. Flying might be your best option.
Of course one way to get more time for some of these is to cut back on Paris, but the net result might just make your whole trip feel squeezed.
I don't have a sense of your priorities. If Normandy is important, you might budget 3 or 4 days there with a car, which would leave you perhaps 3 days to get to Barcelona, if that is set in stone. If the Alps are the thing, make sure to have enough time and felxiblity that inclement weather does not wipe out, say, your one day in Chamonix.
Want to spend a little time in Provence or the Cote d'Azure? Skip the Alps or Barcelona. Etc.
