I like the idea of traveling by train a lot better, since it will leave you with more sightseeing time.
However, are you aware that there are beaches in the Barcelona area? If your mom wants two days on the beach and you have just four days to get to the Rivera, see the Riviera and then get to Barcelona, you're going through an awful lot of churn for just one non-beach day along the Riviera. If you took the beach time near Barcelona, you'd save a lot of travel time, and there's lots to see in Barcelona while you're not at the beach. You could even take a day-trip to Girona for a change of pace.
Believe me, I like the Riviera and the hill towns above it. The area is imminently worth visiting. It's just that from a logistical standpoint on this short trip, I think hitting the beaches near Barcelona is more practical. If you want beach suggestions around Barcelona, post an inquiry in the Spain forum. We have posters who currently live in Barcelona or have lived there in the past; they'll give you the straight scoop.
Here are the comparative rail-transit times (based on current schedules):
Paris Gare de Lyon - Nice Ville: 6 hr.
Nice Ville - Barcelona: 8 hr. 30 mi.
(You might opt to fly this segment, but realistically it's probably still going to take about 5 hours door to door because you need to be at the airport so early.)
Paris Gare de Lyon - Barcelona: 6 hr. 40 min.
As you can see, you save a full of day train travel or 5 hours or so dealing with airports by going straight from Paris to Barcelona.
I hope your mom won't be disappointed in the European beaches at her disposal. Many are rocky rather than sandy. Some of those rocky beaches are quite picturesque to look at; I'm not sure they're so great for swimming. Nearly all beaches convenient to urban areas are mobbed during nice weather. Northern Europeans suffer from long months of minimal sunlight, and they swarm to the southern beaches in the summer. The population of Europe is a lot denser than the population of the US, so the result is more people per square foot of beach--a lot more people. If you Google for photos of beaches in the areas you'll be visiting, I think you'll see flocks of beach chairs laid out in rows just a few feet apart.