Over the years I have developed a special affinity for France. I traveled there with groups and alone in the 70's 80's and 90's and when I started touring with the bike it seemed like a good place to start.
The Loire Tour was by far the best place to start because the biking infrastructure there is some of the best I've ever seen. Hundreds and hundreds of kilometers of well-marked routes, mostly on lightly traveled country roads or special trails, complete with signs for car drivers to "Share the road with bikes". In addition to the plethora of routes there are tons of hotels in the area that cater to bikers, with special bike parking places, etc. I can't recommend the Loire Valley enough as a biking destination - lots to see and do, lovely countryside and of course the food and wine are superb.
I also have a limited experience in the south of France, riding the Canal du Midi from Bordeaux to Sète in 2011 and the Dordogne region and the Lot Valley in 2012. The Lot has a great, well-marked bike route but the Dordogne region is a little less bike-friendly, which isn't too surprising when you consider the hilly countryside. The Canal du Midi was interesting - from Bordeaux to Toulouse the trail was asphalt and well-marked but about 20km south of Toulouse the signage practically stopped and some of the rutty, sandy trail was among the worst I've ever seen. But there were plenty of bike-friendly accommodations and the scenery, food and drink made one forget most of the discomforts.
And Paris... who'd have thought it, but Paris is a blast for bikers. On four different trips I/we have had to traverse through the city with fully-loaded bicycles changing train stations for legs of the journey. There are plenty of fellow bikers and well-marked bike lanes. Naturally, it's a big city with plenty of traffic so one needs a certain amount of self-assertion on the bike. In the end, the biggest difficulty I've had was trying not to run over the dumb tourists that walk out onto the street without bothering to look for traffic. And I ask you, what's more fun than riding your bike down the Champs Elysées??