You can divide France into departments, which total 10. If you subdivide France into larger regions, you are left with 16. That's a bit more manageable. Because the difference between Lot et Garonne or Dordogne, many will care.
Cycling in France in the north is similar to cycling in Limburg. There it is beautifully hilly, you have wide views and, of course, cobblestones. It also includes the coast of Normandy and the busy Ile-de-France region. For many, the highlight of the north is surely Alsace (and the adjacent 'Lorraine'). With the Vosges Mountains, you are always in the right place here. The Grand-Ballon or the Ballon d'Alsace and the Planche des Belles Filles.
In the centre of France, you obviously have the Rhone Alpes region, with all the famous climbs from the Tour de France. But don't forget Burgundy and Comte, all with beautiful cycling areas.
Further south you will find Provence, where you can test your legs not only on the Mont Ventoux, but also around Nice on the Col de Turini or the Madone. If you go cycling in Languedoc, you will cycle through the low mountain range or along the beautiful coast, with the salt flats in between where you can get the original 'fleur de sel'.
The Pyrenees speak for themselves, with Superbagnères, Plateau de Beille, Luz-Ardiden and Peyresourde in addition to the aforementioned major climbs.