When I've booked most of my longer stays I've just used the town website to give me clues and then gone to Google maps and searched "gite" on the map. This brings up all the appratments not just those offered by one company or another and in geographical splender.

If you then click on the dot you normally get both the chain that is renting them but also local contact details. Worse case you might have to email the town's website to get them to call for you.

Google translate in pretty good English to French to be able to send an email. Though I speak both languages.

Annecy is beautiful, but my recollection is that it was a little colder than Grenoble, where I lived in the early '70's. Perhaps because it's further north. And my memory of Grenoble in March is that it is quite cold with periods of snow. Annecy is cold in March (generally speaking), but doesn't really get much snow at all. I remember one March, we left a snowy Grenoble to drive to Paris (actually, we hitch hiked if truth be told) to go to a concert in Paris, and Paris was having a heat wave at the time.

For me, I would consider the south of France, as there are always nice days in March. I'm particularly fond of Juan les Pins in summer and fall, but I imagine it is quite nice in the early spring . . . their winters are very mild. They will be in the upper 50's this week! Next door to Antibes, but the cheaper version. Alternatively, you might consider Le Cannet, just above Cannes, a wonderful little commune sheltered by the mountains, generally dry and warm. The old center has lovely shops and art, such as the Wall of Lovers. And a 10 minute drive down to Cannes.

Annecy wouldn't be my pick either, due to location and weather. You know those surveys, they are measuring things in relationship to what living there is like in terms of services, crime, city functions, taxes, etc. Not really what matters most to a tourist just visiting a couple months.