When is your trip? If it's to be in the summer, consider that you're spending almost all your time at hot destinations.
Have you ever traveled like this before, taking 7 or 8 flights within a month? Airports are inherently stressful, and you're going to lose a lot of sightseeing time with all those flight days.
I think trying to combine Spain, Italy and Greece on one trip is at least one peninsula too many, and I'd encourage you to visit those destinations over the course of two trips rather than cramming them all into one.
You've sketched in more flights than are strictly necessary. You can get from Venice to Rome on a fast train in less than four hours. There are TGVs between Paris and Nice that take less than 6 hours (which I'd prefer to a flight, though not everyone would), and there are some under-5-hour trains between Nice and Milan.
I still think it's too much moving around, but you could travel Paris-Nice-Milan-Venice-Rome-Greece-Barcelona and need to fly only to, from and within Greece. I checked, and there are non-stop flights between Athens and Barcelona. But I'd drop at least Barcelona from this trip. Two days plus a couple of hours is not enough time to do it justice; I wouldn't fly to a country for such a short time.
Alternatively, three days on the Riviera would not be worth two flights to me if I could instead fly straight from Italy or Greece to Barcelona, so Nice is something I'd consider cutting if you want to stick with the original basic route.
It would be better to have more time for Greece, since it's awkward to get to. I'd like for you to see an island that isn't as touristy as Mykonos and Santorini.
In sum: although your time allotments are not crazily short, there are many wonderful places to visit near those cities that would not require so many long train trips or flights.