I'll start with ruling out places:
Normandy and Brittany (really anywhere along the west coast) is generally rainy, windy and cold in the spring. I don't think you would enjoy staying there.
Provence is known for their massive spring winds, the Mistral. A friend went to Provence in the Spring and remembers the wind more than anything else.
I visited Burgundy and Alsace in May. The area is beautiful but I felt I was there too early. Especially Burgundy in early May. It was cold, the vines were barely sprouting and many restaurants in smaller towns weren't open yet. Alsace was better but that was later in May.
I went to Loire in September. I'm really not sure when the area starts warming up? I thought Chinon was a nice place to have a base. It seems older, more authentic, than much of the Loire Valley.
I think south makes sense. It's early for the Riviera but might be a good time to visit outside of peak beach season. I visited the Languedoc area in June and thought it was perfect. The weather was off and on rainy but not cold and I beat the tourist season (every town seemed to be preparing for the onslaught). The Ardeche area is drier than Languedoc/Lot Valley/Dordogne Valley. If they don't have the same problem with the Mistral, you might really enjoy it. I was surprised how much I liked the Ardeche because you don't read much about it in travel guides.