Scored cheap airfare, now what?

For such open-ended questions, you should go to the Watch, Read, listen->Rick's travel articles->France->Suggested itineraries. He has some good suggestions. It's a good place to begin.

Also, do you have the RS France book, or another guidebook? You can go to the library and get several. With 8 days, you don't want to plan a big trip, but it's certainly enough to see some fun stuff.

You can find actual day-by-day temperatures for February 2017, February 2016, February 2105, etc., on wunderground.com. I've linked to Nice's data for February 2017. I've just noticed that the Calendar tab shows the precipitation by day, as well as temperature. Nice doesn't look bad at all, though it appears that you must prepare for some rain at that time of year. Take a good waterproof jacket with a hood. Waterproof shoes would be handy, too.

In addition to being a great transportation hub for other destinations along the Riviera, Nice has a lot of museums that--if you're interested--will keep you occupied on the days with the worst weather. Opening hours at a lot of places are cut back in the winter, and some places are closed two or even three days a week. It will be important to get hold of a good guide book, make a list of the sights you want to see, and then check the individual websites to form a plan of attack. Most guide books assume you are traveling between late spring and early fall; they may not have the information you will need for a mid-winter trip.

You might consider splitting your time between Nice and another, smaller city. There are many lovely options, but I really liked Menton, which is said to be the warmest place along the coast. It has a couple of really good gardens as well as a largish, picturesque historic district. Very touristy in the summer but I'm sure saner in February. Menton is very near the Italian border, so you could visit somewhere like San Remo.

I found Normandy an excellent area to visit in July, when much of the rest of France was miserably hot. Wunderground's data for Caen shows that the temperature probably won't be bitterly cold in February, but you probably shouldn't expect to see the sun. Given how short the days are in February anyway, I'd find Normandy depressing at that time of year, but I know most people don't need sunlight to the degree I do. You can visit Normandy by train and bus (I did, plus I took a very good one-day D-Day tour by van), but it would be great to have a car in that area.

I don't care for palaces so can't comment on the Loire.

Edited to add: I think you should be able to find great deals on Riviera lodgings in February. Even in May, hotel rates in Nice were considerably below the mid-summer level.

Having been there in February for sure count on rain. The Loire is nice for castles. You can base your self in Blois or Amboise both have castles and take trips from to see the castles at Chambord and Chenonceaux. I was in Normandy/Brittany in January and based at St. Malo covered a visit to Mt St Michel and then based at Bayeux (lovely town) took a tour from there to the D-Day beaches. It rained but the weather was better in Normandy/Brittany than in Paris. Normandy and Brittany area are more known for cider and calvados than wine so maybe consider that but obviously has great scenery art and history. I am landing in Paris December 27-January 6 and having been to all the places you are considering I am also still trying to figure out where I want to go without having to fly somewhere.

In your case I would do the Loire it is short ride from Paris/

The Riviera has strikingly better weather, particularly the micro-climate in Menton, which is on the Italian border. It’s a popular wintering spot for Europeans. Your dates just border the Menton Lemon Festival, Fête du Citron, which begins on the 14th. Having lived in the north for many years and visited family on the Riviera in winter, I know where I’d go.

That time of year you'd be wise to stick to towns big enough to have indoor attractions, not to mention cafes to duck into to warm up or get out of bad weather. You want places big enough that they do not shut down when the tourists leave.

I recommend Lyon, not exclusively but for 3 or 4 days. It's enroute to the coast, though I would not assume that coastal weather is going to be the best you can do.

Bets, the info I'm finding online says that Menton's lemon festival begins on February 17 next year.

You are correct, thank you, the 17th. It’s too bad to miss it by hours, but it makes it easier to find a place to stay.

I'd bet that some hotels and restaurants will be closed for February, due to storms.
The weather will be absolutely awful in Normandie in February.
I'd go to the Loire valley to see the chateaux or Lyon for wine and food and history.

Menton wasn't my favorite place on the Riviera but it isn't touristy and the microclimate sounds great.

If it was my trip, I'd fly from Orly to Nice, a little over an hour flight. Air France plus at least one other carrier run that route, about $50 each way, maybe cheaper in February. You can then catch a train to Menton. The train station is about a mile from the airport, so you might need to catch a cab. It was walkable for me, but I carry only a light shoulder bag. The train has about a half dozen stops before Menton, including Monaco. Figure about 1/2 hour to 45 minutes once you're on the train. I'm not sure how often the trains will run in February? I'd check out Airbnb as a lodging option.

My personal favorite is Antibes. For me It had the right mix of marina, beach, smaller town, medieval center, cafes, galleries... In February the sandy beach in Antibes vs. the pebbles in Menton won't matter and Menton will have more restaurants to chose from.