I don’t really understand why you want to fly up to Dublin for 3 nights. (OK, maybe it’s nice, but…) And if you insist on Dublin, why go down to Paris first???

I would take at least 2 nights in Paris. It has more to offer than for example Barcelona or Dublin and a LOT more than Nice.

And yes, Barcelona has a great nightlife. And it’s a nice place to spend some time. So I wouldn’t cut back on your number of nights there.

But Nice????!!!??? If you want to enjoy a bit of the south of France, spend some days in Avignon or Aix-en-Provence. Nice is a seriously overrated place IMO.
Also consider that Barcelona – Rome can be done on low-cost airlines. If you want to pass by the south of France you’ll be complicating your itinerary a lot. (Go by train, with a lot of connections, or drive…)