Weekend trips in Europe starting from Nice,France

I'll be in southern France next spring myself and very much look forward to the suggestions you receive from others.

I assume you realize that if you're from the US or Canada you'll need a visa to stay in France for more than 90 days (which includes both the arrival day and departure day).

Libby, The train route east and west of Nice is picturesque along the coast, but not fast. You won't get to a high speed until Marseille (west) or Genoa (east).
But, Nice has an airport with lots of flights by budget airlines. The airline with the most destinations is Easyjet, who fly to:
Amsterdam, Barcelona, Basel, Berlin–Schönefeld, Bordeaux, Brussels, Geneva, Lille, Lisbon, Liverpool, London-Gatwick, London-Luton, London-Stansted, Marrakech, Nantes, Naples, Paris-Charles de Gaulle, Paris-Orly, Rome-Fiumicino, Toulouse, Venice
Seasonal: Belfast-International, Bristol, Cagliari, Edinburgh, Hamburg, Mykonos, Newcastle upon Tyne, Olbia, Palma de Mallorca

That should give you a few options for short breaks.
Full list here: https://en.wikipedia.org/wiki/Nice_C%C3%B4te_d%27Azur_Airport#Passenger

From Nice to neighboring countries by train takes, for instance, 9 hours to Barcelona, 6-7 hours to Pisa in Italy, or 9 hours to the German/Swiss border area at Basel. There are no overnight trains on these routes. Flying to any of those same destinations is usually both faster and cheaper. In addition to Easy Jet, see www.skyscanner.com for more flights.

Train tickets are not cheap for long distances, although prices are better if you lock in reserved tickets early (available starting about 3 months in advance). Rick’s Train Travel Time & cost Map gives you an overview of faster train travel times in hours, as well as regular (full-price) 2nd-class fares. How to Look Up Train Schedules and Routes Online gives you the DB train schedule link for all of Europe and tips for using it.

I was considering a trip there in February and found out that there's a lot going on during Carnival (roughly Feb 10-28) in Nice and nearby Menton has a big lemon festival then. Try googling "provence festivals."