Thanks for all the tips, guys. We'll have to prioritize and consider what would make the most sense definitely. I figured the itinerary I proposed would likely be too aggressive but wanted to get a feeler.
Flying to Nice from Paris sounds like it would work. But I'm starting to re-think Nice to begin with. Of course, I think it's only because we were wanting to hit both France and Italy that I wanted to try to get more of France in the mix. As far as Pisa - I've done it before where I've made it less-than-a-half-day trip and stopped off to see the Leaning Tower for a few hours, then hopped on the train to La Spezia (coming from Siena). Definitely doable - I don't intend to spend more than several hours in Pisa anyway.
Any suggestions on other cities in France to visit if I were to cut out Nice all together? Or would the recommendation be just more time in Paris? Then fly to directly to Pisa or something?