Due to work March is the only time we have to travel. In which areas of Europe would the attractions be accessible and enjoyable at this time of year?
March is a good time to travel to places that get really warm in summer.
I have traveled to Sicily and Andalusia on different trips during March and found the weather agreeable.
If you have a desire to see Holland abloom, Keukenhof opens it lavish bulb displays on March 21, 2020. https://keukenhof.nl/en/ From Holland you could travel south to enjoy spring in France or take a flight to somewhere much further south and warm.
Oh yes, I agree with seeing Keukenhof as close to the end of March that you can.
I was in Paris at the end of March and it was excellent. I thought the temperature was good but I can tolerate some cold. Your profile doesn't yet say where you live so if you are from Florida you might think it still feels like winter, lol! I also did Rick's Belgium and Holland tour in April and it was good. A few days were chilly and windy but otherwise it was a terrific time to go.
Big cities are good in any weather. I'd skip Switzerland in March unless you are a skier.
What countries are of interest to you?
Southern Spain or Italy. Having been to Keukenhoff in March 2016 and then seeing it again after things have had longer time to bloom in the 2nd week of May 2019, I would not go there.
It also depends on what you want to do. Hiking in central or Northern Europe may not be best unless you want cold conditions. Likewise, beach towns most places will be very quiet - it may be nice weather but not lie on the beach weather. But going to a city where you mainly go inside museums or restaurants weather doesn’t matter so much.
Just going on time of year I’d stay south. Rome, southern Spain, Sicily, Lisbon, Athens. It will likely be pleasant temperatures, and there’s a lot to do any time of year.
Or stick to a big city where if the weather is bad you can spend that day inside museums/shopping/theater/restaurants. London and Paris come to mind first.
Portugal. Portugal. Portugal (in that order).
Another vote for Andalucia, the perfect time to visit, or if the cold is your preference - skiing in the Pyrenees.
I would choose Italy. We went in March many years ago and it was wonderful. Not hot and not crowded. Many of the shops were decorated for Easter.
Spain would be another great choice.
I was in Spain in March about 3-4 years ago and it was wonderful. Check out Las Fallas Festival in Valencia. The orange trees were in bloom everywhere, the scent of orange blossoms was heady. Barcelona, Madrid, Costa Brava, Andalucia - all are great, low season prices and fewer crowds.
Italy is another excellent choice, anywhere in the country. And of course Portugal as well. Greece might be an option though some of the popular islands may still be mostly shut down. It's a good time to see Istanbul.
I was on the French Riviera this year in mid-March and it was wonderful.
London, Paris, Berlin, Vienna, Budapest, Amsterdam . . . any major city is always a good choice.
We lived in Augsburg, Germany for four years and loved Germany, but the cold season in Germany is long. In early Spring we were always eager to go south over the Alps to Italy were we could see more of the sun and warmer weather.
Greece is nice in March. One thing, many of the beach areas, even in the Med, during March and early April, the water would be a bit cold to go swimming.
Fire Festival in Valencia Spain will be March 15-20, 2020. I'd include that, Seville and Granada for a nice trip.
Things I'd recommend adding if you have time: Ronda, Antequera (passage tombs and museum), Gibraltar, Jerez, Cordoba,
As others have said southern Spain is a good bet. The weather is usually quite nice plus it's one place that I wouldn't want to go to in summer due to the extreme heat. I'm not bothered by heat in general and often go to southern Europe in summer, but southern Spain is much hotter than other places so March is a good time to visit. I've been to most of Italy in March and you can get some lovely weather but also some pretty cool, rainy weather. I've also spent quite a few trips in March in Paris and London and while no guarantees of great weather I've certainly had some nice enough (60s, sunny, flowers budding out) plus cities have the advantage of lots to do on the days that it's not so nice out.
The only things I wouldn't do are rural areas in northern Europe or places that are really just summer destinations (like the Greek islands, although I've read lots of trip reports to the Greek mainland that sounded OK at that time of year).
I only travel to Europe in early March every year. I prefer this because it is so much less crowded (any country you choose) and also much cheaper. The catch is that the weather is sketchy, the attractions have shorter hours and if any attraction is in need of repairs or restorations, this is the time of year when they do it. For me, the positives far outweigh the negatives