I rode across France last year (June is the wettest month in France I discovered) and it is a great place to ride a bike. I rode a loop around Switzerland this year and it, too, is a great place to bike with well marked cycle paths that often are car-free.
It took me 26 days to go from Paris (CDG airport) to Normandy down to the Dordogne River and up it, up the Lot, and up the Tarn and then over to Avignon. I was doing 50-70 miles/day and resting every 4-5 days. I have written up a journal of that ride
. It includes my planning, route, and lots of pictures. It may give you some idea of bike touring in France.
I am in the process of writing up my Switzerland trip. While it would be hard to spend 4 weeks bike touring only in Switzerland, the 2 weeks of riding I did there involved both hard climbs and stunning scenery. You can see some of my best shots here
Since France and Switzerland are next to each other, there is no reason you can't do both of them. You could do a big loop and start and end in Paris.
Another idea might be something like heading east from Paris, into Germany, down through the Black Forest to Basel, along Swiss National Route 7 to Geneva, and then go west or south back into France. You could fly out of Nice or Marseille, or take a train or ride back to Paris. You could also take a different Swiss Route and end up somewhere in Italy.
While I've been to Italy several times, I've never bike toured there. As you suggest in your original post, you could go from Paris to Rome, but that may require more time or longer days.
Whatever you do, be sure to ride through some of gorges in France. They are spectacular.
Any of these sound good?