10 days in the south of France by car in March.

I suggest you pack something like a fleece vest and gloves, maybe a hat or warm scarf. Spain is not particularly warm at that time of year; nor is France.
The area around Perpignan has much to see and do. Some towns worth visiting are Collioure, Ceret, Castelnou. Many Romanesque churches and abbeys are scattered through the region. It was also home to quite a few modern artists for parts of their lives, including Maillol, Picasso, Matisse, and Charles Rennie Mackintosh.

Uniqlo or other lightweight down jackets or vests pack into tiny sacs and weigh very little. Mine has become my go-to jacket for a range of weather conditions depending on what I layer with it.

Read up on the mistral. From what I learned planning my visit (10 days, mid-late March this year), it blows icy cold through the western part of southern France, the eastern part is rarely affected at all. Indeed I had a chilly day in Marseille (2N). I spent most of my time between Nice (5N) and Menton, taking the train along the coast, and then the inland areas as far as Vence and Tourettes, stayed in St. Paul de Vence (3N). Then I flew budget from Nice to Barcelona.

I enjoyed exploring the villages away from the coast, but I also enjoyed the beach-y areas. I loved Villefranche. While there are a lot of tourist shops and quite a few tourists, especially in Nice, there were no crowds anywhere - except for the Irish pubs in Nice on St. Patrick's day. I think St Paul gets tons of tourists, even in March, but I wasn't there from mid-morning until late afternoon, when it was incredibly quiet and the only tourists were the few like me who were staying there. It is a challenge with a car, but worth the inconvenience. And, except for the hours with the mistral in Marseille (when a fleece sufficed), it was warm and sunny everywhere.

I would be shocked if you don't run into temperatures below 13C. Maybe you'll see that as a high every day. I arrived in northern Andalucia on April 10 this year. I had two or three mornings when it was 8C or 9C at 9 AM, and it didn't get all that warm. If you're looking at average temperatures, I recommend that you check out the actual, day-by-day historical weather data on timeanddate.com. Keep in mind that you may be outdoors at 8 or 9 AM and will almost certainly still be out and about some evenings at 9, 10 or 11 PM, given the extremely late meal hours in Spain.

I use a 3-in-1 coat when I've traveled, which is warm when together or you can break apart if you just need the rain jacket or down jacket. I also have a thin Columbia hoodie that I can layer on top and provides more warmth. The key is really to layer. If you have a few more "under shirts" or whatever you will wear against your skin, you can re-use those outer layers without needing to wash repeatedly -- a vest might also help.

As for destinations, we spent six nights in Provence and loved it. Our base was L'Isle sur-la-Sorgue and we took day trips to the towns -- Arles, Avignon, Usses, the Pont du Gard, Rousillion, Gordes, Las Baux, and even a day trip down to Cassis on the Mediterranean. While you were in Dijon, if you didn't get into Burgundy/Beaune (and if even more so if you love wine), then I would suggest there -- these two areas were our favorite. But, we were there in May, so I can't speak to the weather aspect. Hugging the coast line might also make it warmer, might be worth checking average temps.

What are your interests? Architecture, food, natural scenery, history, art, culture, etc? This will shape your recommendations. I wouldn't describe anything along the way as ho-hum -- that is pretty subjective. However, I will say in March some of the areas of the South may still be closed for the winter (shops, restaurants, hotels, etc) They generally open up in about April. This is of course not true of the larger towns and cities, and major tourist towns. The weather can also be impossible to predict (as noted, the coast will be warmer).

Thanks, everyone, for your responses. We have plotted all of your suggestions on the map and decided to take the train from Barcelona to Perpignan and follow your suggestions over to Monaco. We will fly from Nice to Paris then fly home. (I knew my ho-hum comment would draw a response!) We enjoy history, architecture, quaint, food and views of all sorts, so I think it will perfect. Weather really doesn't concern us too much. Rain or sun is good, but no snow! Thanks for the Uniqlo mention. We will check that out. We will be south of Malaga for February, then gradually move up to Barcelona. We hope to miss the mistral. Thanks for the heads-up on that. We also picked up Rick's book on Provence to get his tips on accomodations, etc. We appreciate so much your time to reply. Thank you very much.

You might consider an extended stop near Avignon/Nimes/Pont du Gard, to satisfy some of your interest list, before hitting your quaint quotient in the smaller villages. Since you've already been to Carcassonne, you may want to hit Couilloire and then head east.

On the Cote d'Azur, besides Eze you might consider Villefranche-sur-Mer, Cap Ferrat/Villa Ephrussi and St. Paul de Vence as noted. In Nice, make sure to go to the top of Castle Hill for the view and hit the old town and Promenades.

Yes, we will do that. Our France portion will now be 15 days so we have time to daytrip from both Nimes and Avignon. We welcome any further suggestions. Thanks!

If you are heading east of Marseille, the Ile de Porquerolles would be lovely on a sunny day in March. Short ferry, beautiful hiking trails. Non touristy in March.

Thanks, Barbara. We will now overnight in Hyeres and take your suggestion.

SUMMING UP we are thinking Perpignan 2 nights, Nimes 3, Avignon 3, Cassis 2, Hyeres 1, Nice 4...Stop me now if it looks wrong, please. Thanks again everyone.

Hello from Wisconsin,
Inland a bit from Narbonne is Cather country. Not Willa Cather, but a deemed heretical religious group. Pretty much burned to death by "good" Catholics. Some impressive castles. Read up on the Cathers and you might be shocked that an off shoot of mainstream Catholicism would be so down on a love based interpretation of the Bible. Once you know about them, you want to see where it all happened.

wayne iNWI

I spent a couple of nights in Hyeres in May 2017 so I could go to Porquerolles. I liked Hyeres for its historic center and lack of foreign tourists. I wad underwhelmed by Porquerolles and thought it didn't really justify the time required to see it, especially for a car-less American. We have an abundance of sandy beaches at home, most of them not as crowded as what Europeans have to tolerate. I think most Americans not spending a great deal of time in southern France would get greater enjoyment from other types of destinations in March. It's not that Porquerolles is a bad place; it's just not Antibes, Nice, etc. How much of your limited vacation time are you willing to devote to walking on or looking at an empty sandy beach?

I must warn you that the wind was really whipping around on the island in May; if that happened in March (when it might also be rainy and chilly), I think it could be really unpleasant. I don't believe my experience was unusual, because the only map available at the island tourist office was printed on a sort of plasticized paper. I wondered why that was necessary as I handed over my 3 euros. But then the wind started to blow, and I had my answer.

You should check on the ferry schedule. March is way off season..

I think wayner means "Cathar" country...it's a bit of a drive from Narbonne but interesting if the weather cooperates. Lots of castles in various states of ruin perched on high peaks.
Definitely bring winter clothing...the mistral winds down there can be fierce and unforgiving.
My favorite towns and things to see in the area are...
Pezenas
Narbonne
Collioure
Beziers
The Cevennes - beautiful caverns and gorges
St. Guillaume le Desert
Wine! Abbaye de Valmagne is a favorite winery
Sete
The marine archeaology museum in Agde
You will definitely be there in the off season but still should be able to see a lot!