kbarch

Well, Googling "cycle tour Europe" is one place to start.
Of course organized cycling tours typically last several days, so if that's what you'd like to do, depending on how long you intend to stay there, it may not mesh well with traveling with your brother.
If this really is a shared vacation and you want to play it by ear, try searching for a specific place to make your "base of operations" first. Take a look at a map. If you want to mix in some urban/cultural experience, decide on one or two cities you'd REALLY like to visit, then consider the surrounding geography. Find a SMALL town about an hour or two away from the city/cities of interest, in the direction of the most interesting geography, but no closer to any major cities. Look for hotels/inns in or near that small town. A "resort," more or less modest depending on your budget, can be ideal.
I didn't pick this one - the tour organizer did - but here's an example: our base of operations was in Borso del Grappa, which is about 80km north of Venice. The hotel had a good restaurant, catered to outdoorsy, active travelers, and was located adjacent to a parasailing landing field. Garden Relais - Le attività Being at the foot of the Dolomites meant that, depending on which way you headed, you had your choice of scenery and could ride through mountains, hills or lightly rolling plains. Belluno, Trento, Vicenza, Padova and Verona were all within as easy distance as Venice, as were innumerable other interesting towns. Bassano del Grappa, an extremely charming town, was just a few minutes' bike ride away, as were Asolo, Maser, Marostica....
I don't know France so well, but suspect there are similar places around Avignon and Aix (maybe Cavaillon?) that provide similar variety, relative convenience and bon marché.