Travel from Granada to Valencia

Personally, I think your best bet would be to rent out a car and directly drive to Valencia through Murcia, which is about 5 hrs.

You could also take the AVE high speed train, but would first require you to take the ALSA bus to Cordoba and then catching the AVE train back to Madrid and then hopping on the AVE east to Valencia, about 7 hrs.

Another option could be taking the ALSA bus from Granada to Valencia which includes 4 stops and comes in at 8 hrs.

Then again you could try to fly which is about 3 hrs but is more pricey.

I think because of its size and shape, Spain is on sort of a spoke system for train travel. A lot of the routes radiate out from Madrid. (France is similar) For a traveler, its frustrating because it does seem reasonable to just be able to go from Granada to Valencia. And in addition, Granada is tricky right now because they really don't have trains at all. The Granada "train" travel is a bus ride to Antequera where you then catch a train. For us, it added at least an hour of travel time. I would look at Vueling and consider flying. If you book in advance you can get good rates. Or look at renting a car. I've been happy with rates and service with Autoeurope or bus.

Consider making Toledo your first stop, then travel back through Madrid.

ie. Toledo; Córdoba; Sevilla; Granada; Madrid; Valencia; Barcelona and then back to Paris.

We didn't go to Paris this trip, but we flew to Granada -> Sevilla -> Cordoba -> Madrid -> Valencia -> Barcelona. After flying to Granada we traveled by train.