One region I would suggest you avoid in BOTH countries is the Riviera. Along most of the French Riviera, there is simply too much traffic, esp. in summer, for enjoyable cycling, IMHO. The Italian Riviera was even worse. The coast from Genoa to the French border is completely built up. Inland Provence was much more pleasant on a bike than the Cote d'Azur.
I admit that I am partial to cycling in France, but this may be influenced by the fact that I speak French well, but don't really speak Italian--though I'm able to converse poorly. Having said that, Italians don't expect tourists to be able to speak Italian. But trying to be objective concerning your original question, I've found that most of France (the Riviera being an exception) has a wonderful network of secondary roads with very little traffic. I found that this was not as true in Italy, in part because it's a much more mountainous country and there are simply fewer roads in mountainous areas.
I've biked a fair amount in Provence & the Alps and enjoyed it. I have to say, however, that my very favorite region for bike touring, not just in France, but in the entire world, is the area in SW France near the Lot, Cele, & Dordogne River valleys. Gorgeous scenery, wonderfully quiet roads, lovely medievals villages and towns, and a wealth of interesting sights including many castles and caves that are open to the public. Also, some of the best cooking in France, and that is saying something. But, you'll certainly eat well in Italy, too.
And if you end up in SW France, it's a short hop on a train or a few days on a bike to reach the Pyrenees and the delights of the Col du Tourmalet, which I rode up once. Since Alpe d'Huez interests you, the Tourmalet might, too. As for l'Alpe d'Huez, the road starts from the western side of the Col du Lautaret road. The ride from Briancon up the Lautaret isn't too difficult, and the descent toward Grenoble and the turnoff for l'Alpe d'Huez is superb; lovely scenery, gentle, long descent with little braking required, until you reach the built-up outskirts of Grenoble.
If you go riding in Provence, you might want to visit the historic synagogues in Carpentras, Cavaillon, & Avignon.