Nice sounds like a great time in March. I don't know how good the
weather is that time of year as I was there in May but I don't think it would
be too bad. I found Nice a good central location to travel the rest of the
French Riveria. There are 40 trains going either direction a day. Cannes is
about 40 min by train and Monaco is about 20 min. You might find some shops
and restaurents closed as it might be off season.
I sent a travelogue about my trip to the French Rivera in the summer. If
you want a copy let me know and I will email it too you.
Have a great time!
Tom, London, Canada